SAT Math Flashcards - SAT Math
Card 0 of 103
Effect of multiplying by $0 < a < 1$ in $y = a f(x)$.
Effect of multiplying by $0 < a < 1$ in $y = a f(x)$.
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Vertical compression by factor $a$.
Vertical compression by factor $a$.
Effect of multiplying the function by $a > 1$ in $y = a f(x)$.
Effect of multiplying the function by $a > 1$ in $y = a f(x)$.
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Vertical stretch by factor $a$.
Vertical stretch by factor $a$.
Expand $(x - 2)(x + 7)$.
Expand $(x - 2)(x + 7)$.
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$x^2 + 5x - 14$.
$x^2 + 5x - 14$.
Expand $(x + 5)^2$.
Expand $(x + 5)^2$.
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$x^2 + 10x + 25$.
$x^2 + 10x + 25$.
If linear and exponential start equal, which is larger after many intervals?
If linear and exponential start equal, which is larger after many intervals?
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The exponential model.
The exponential model.
In $y = 50(1.05)^t$, what happens if $r$ increases from 0.05 to 0.08?
In $y = 50(1.05)^t$, what happens if $r$ increases from 0.05 to 0.08?
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Growth is faster; values increase more rapidly over time.
Growth is faster; values increase more rapidly over time.
Simplify -2(3x - 5) + 4x.
Simplify -2(3x - 5) + 4x.
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$-6x + 10 + 4x = -2x + 10.$
$-6x + 10 + 4x = -2x + 10.$
Simplify $(2x)^2$.
Simplify $(2x)^2$.
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$4x^2$.
$4x^2$.
Simplify $(x + 3)(x - 3)$.
Simplify $(x + 3)(x - 3)$.
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$x^2 - 9$.
$x^2 - 9$.
Simplify $|-8|$
Simplify $|-8|$
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8
8
Simplify $|3-9|$
Simplify $|3-9|$
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6
6
Simplify $|3x|$
Simplify $|3x|$
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$3|x|$.
$3|x|$.
Simplify $|5|$
Simplify $|5|$
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5
5
Simplify $|x|^2$
Simplify $|x|^2$
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$x^2$.
$x^2$.
Simplify $f(x) = (x + 2)^2 - (x - 2)^2$.
Simplify $f(x) = (x + 2)^2 - (x - 2)^2$.
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$(x^2 + 4x + 4) - (x^2 - 4x + 4) = 8x$.
$(x^2 + 4x + 4) - (x^2 - 4x + 4) = 8x$.
Simplify $f(x) = (x + 3)^2 - 9$.
Simplify $f(x) = (x + 3)^2 - 9$.
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$x^2 + 6x$.
$x^2 + 6x$.
Simplify 3(x - 4) + 2(x + 5).
Simplify 3(x - 4) + 2(x + 5).
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3x - 12 + 2x + 10 = 5x - 2.
3x - 12 + 2x + 10 = 5x - 2.
Simplify 4(2x + 3) - 2x.
Simplify 4(2x + 3) - 2x.
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$8x + 12 - 2x = 6x + 12.$
$8x + 12 - 2x = 6x + 12.$
Simplify and solve: $5(2x - 3) < 15$.
Simplify and solve: $5(2x - 3) < 15$.
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$x < 3$.
$x < 3$.
What is $\cos 0^{\circ}$?
What is $\cos 0^{\circ}$?
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1
1
What is $\cos 60^{\circ}$?
What is $\cos 60^{\circ}$?
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$\tfrac{1}{2}$.
$\tfrac{1}{2}$.
What is $\sin 30^{\circ}$?
What is $\sin 30^{\circ}$?
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$\tfrac{1}{2}$.
$\tfrac{1}{2}$.
What is $\sin 90^{\circ}$?
What is $\sin 90^{\circ}$?
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1
1
What is $\tan 0^{\circ}$?
What is $\tan 0^{\circ}$?
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0
0
What is $\tan 45^{\circ}$?
What is $\tan 45^{\circ}$?
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1
1
What type of change occurs in an exponential model?
What type of change occurs in an exponential model?
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Constant percent (multiplicative) change.
Constant percent (multiplicative) change.
Which grows faster long-term: linear or exponential?
Which grows faster long-term: linear or exponential?
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Exponential.
Exponential.
End behavior of even-degree polynomials when $a_n < 0$.
End behavior of even-degree polynomials when $a_n < 0$.
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Both ends go down as $x \to \pm\infty$.
Both ends go down as $x \to \pm\infty$.
End behavior of even-degree polynomials when $a_n > 0$.
End behavior of even-degree polynomials when $a_n > 0$.
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Both ends go up as $x \to \pm\infty$.
Both ends go up as $x \to \pm\infty$.
End behavior of odd-degree polynomials when $a_n < 0$.
End behavior of odd-degree polynomials when $a_n < 0$.
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Rises left, falls right.
Rises left, falls right.
End behavior of odd-degree polynomials when $a_n > 0$.
End behavior of odd-degree polynomials when $a_n > 0$.
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Falls left, rises right.
Falls left, rises right.
Factor $x^2 - 2x - 15$.
Factor $x^2 - 2x - 15$.
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$(x - 5)(x + 3)$.
$(x - 5)(x + 3)$.
Factor $x^2 - 49$.
Factor $x^2 - 49$.
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$(x - 7)(x + 7)$.
$(x - 7)(x + 7)$.
Factor $x^2 + 5x + 6$.
Factor $x^2 + 5x + 6$.
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$(x + 2)(x + 3)$.
$(x + 2)(x + 3)$.
Factoring rule for $x^2 - 6x + 9$.
Factoring rule for $x^2 - 6x + 9$.
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$(x - 3)^2$.
$(x - 3)^2$.
Factoring rule for $x^2 - 9$.
Factoring rule for $x^2 - 9$.
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$(x - 3)(x + 3)$.
$(x - 3)(x + 3)$.
Factoring rule for $x^2 + 6x + 9$.
Factoring rule for $x^2 + 6x + 9$.
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$(x + 3)^2$.
$(x + 3)^2$.
Sum and product of roots of $ax^2 + bx + c = 0$.
Sum and product of roots of $ax^2 + bx + c = 0$.
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Sum $= -\frac{b}{a}$, Product $= \frac{c}{a}$.
Sum $= -\frac{b}{a}$, Product $= \frac{c}{a}$.
What is a polynomial?
What is a polynomial?
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An expression made up of terms in the form $a_nx^n + a_{n-1}x^{n-1} + \dots + a_1x + a_0$, where coefficients $a_i$ are constants and exponents are nonnegative integers.
An expression made up of terms in the form $a_nx^n + a_{n-1}x^{n-1} + \dots + a_1x + a_0$, where coefficients $a_i$ are constants and exponents are nonnegative integers.
What is a zero of a polynomial?
What is a zero of a polynomial?
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A value of $x$ that makes the polynomial equal to 0.
A value of $x$ that makes the polynomial equal to 0.
What is the constant term in a polynomial?
What is the constant term in a polynomial?
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The term with no variable, usually $a_0$.
The term with no variable, usually $a_0$.
What is the degree of a polynomial?
What is the degree of a polynomial?
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The highest exponent of $x$ with a nonzero coefficient.
The highest exponent of $x$ with a nonzero coefficient.
What is the leading coefficient in a polynomial?
What is the leading coefficient in a polynomial?
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The coefficient of the term with the highest power of $x$.
The coefficient of the term with the highest power of $x$.
What is the relationship between zeros and factors?
What is the relationship between zeros and factors?
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If $x = r$ is a zero, then $(x - r)$ is a factor of the polynomial.
If $x = r$ is a zero, then $(x - r)$ is a factor of the polynomial.
Factored form of a quadratic
Factored form of a quadratic
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$y = a(x - r_1)(x - r_2)$, where $r_1$ and $r_2$ are the roots.
$y = a(x - r_1)(x - r_2)$, where $r_1$ and $r_2$ are the roots.
Find the axis of symmetry for $y = x^2 - 6x + 5$.
Find the axis of symmetry for $y = x^2 - 6x + 5$.
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$x = 3$.
$x = 3$.
Find the vertex of $y = (x - 4)^2 + 1$.
Find the vertex of $y = (x - 4)^2 + 1$.
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$(4, 1)$.
$(4, 1)$.
Find the vertex of $y = x^2 - 6x + 5$.
Find the vertex of $y = x^2 - 6x + 5$.
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Vertex $(3, -4)$.
Vertex $(3, -4)$.
Formula for the axis of symmetry of $y = ax^2 + bx + c$.
Formula for the axis of symmetry of $y = ax^2 + bx + c$.
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$x = \frac{-b}{2a}$.
$x = \frac{-b}{2a}$.
Formula for the vertex $y$-coordinate using coefficients.
Formula for the vertex $y$-coordinate using coefficients.
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$y = c - \frac{b^2}{4a}$.
$y = c - \frac{b^2}{4a}$.
How does $a$ affect the direction of a parabola?
How does $a$ affect the direction of a parabola?
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If $a > 0$, it opens upward; if $a < 0$, it opens downward.
If $a > 0$, it opens upward; if $a < 0$, it opens downward.
How does the rate of change of a quadratic function behave?
How does the rate of change of a quadratic function behave?
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It changes linearly with $x$ (not constant).
It changes linearly with $x$ (not constant).
If $y = -x^2 + 4x + 5$, find the vertex.
If $y = -x^2 + 4x + 5$, find the vertex.
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Vertex $(2, 9)$.
Vertex $(2, 9)$.
If $y = -x^2 + 4x + 5$, what is the axis of symmetry?
If $y = -x^2 + 4x + 5$, what is the axis of symmetry?
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$x = 2$.
$x = 2$.
If $y = 2(x + 1)^2 - 8$, what is the vertex?
If $y = 2(x + 1)^2 - 8$, what is the vertex?
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$(-1, -8)$.
$(-1, -8)$.
If minimum=3 and maximum=27, what is the range?
If minimum=3 and maximum=27, what is the range?
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$24$.
$24$.
Solve $2x^2 = 50$.
Solve $2x^2 = 50$.
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$x^2 = 25 \Rightarrow x = \pm5$.
$x^2 = 25 \Rightarrow x = \pm5$.
Solve $x^2 - 4x - 5 = 0$.
Solve $x^2 - 4x - 5 = 0$.
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$(x - 5)(x + 1) = 0 \Rightarrow x = 5$ or $x = -1$.
$(x - 5)(x + 1) = 0 \Rightarrow x = 5$ or $x = -1$.
Solve $x^2 + 2x - 15 = 0$.
Solve $x^2 + 2x - 15 = 0$.
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$(x + 5)(x - 3) = 0 \Rightarrow x = -5$ or $x = 3$.
$(x + 5)(x - 3) = 0 \Rightarrow x = -5$ or $x = 3$.
Solve $x^2 + 7x + 10 = 0$.
Solve $x^2 + 7x + 10 = 0$.
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$(x + 5)(x + 2) = 0 \Rightarrow x = -5$ or $x = -2$.
$(x + 5)(x + 2) = 0 \Rightarrow x = -5$ or $x = -2$.
Solve $x^2 = 16$.
Solve $x^2 = 16$.
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$x = \pm4$.
$x = \pm4$.
Solve using the quadratic formula: $x^2 + 3x - 10 = 0$.
Solve using the quadratic formula: $x^2 + 3x - 10 = 0$.
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$x = \frac{-3 \pm \sqrt{3^2 - 4(1)(-10)}}{2} = \frac{-3 \pm 7}{2} \Rightarrow x = 2$ or $x = -5$.
$x = \frac{-3 \pm \sqrt{3^2 - 4(1)(-10)}}{2} = \frac{-3 \pm 7}{2} \Rightarrow x = 2$ or $x = -5$.
Standard form of a quadratic equation
Standard form of a quadratic equation
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$y = ax^2 + bx + c$.
$y = ax^2 + bx + c$.
Vertex form of a quadratic
Vertex form of a quadratic
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$y = a(x - h)^2 + k$, where $(h, k)$ is the vertex.
$y = a(x - h)^2 + k$, where $(h, k)$ is the vertex.
Vertex of $y = |x + 4| - 5$
Vertex of $y = |x + 4| - 5$
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$(-4, -5)$.
$(-4, -5)$.
What does a negative discriminant mean?
What does a negative discriminant mean?
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No real roots (two complex roots).
No real roots (two complex roots).
What does a positive discriminant mean?
What does a positive discriminant mean?
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Two distinct real roots.
Two distinct real roots.
What does a zero discriminant mean?
What does a zero discriminant mean?
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One real root (repeated).
One real root (repeated).
What is the definition of the discriminant?
What is the definition of the discriminant?
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$D = b^2 - 4ac$.
$D = b^2 - 4ac$.
What is the maximum value of $y = -2(x + 3)^2 + 5$?
What is the maximum value of $y = -2(x + 3)^2 + 5$?
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5 (occurs at $x = -3$).
5 (occurs at $x = -3$).
What is the minimum value of $y = (x - 4)^2 + 1$?
What is the minimum value of $y = (x - 4)^2 + 1$?
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1 (occurs at $x = 4$).
1 (occurs at $x = 4$).
What is the quadratic formula?
What is the quadratic formula?
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$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.
$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.
What is the vertex of $y = -3(x + 1)^2 + 4$?
What is the vertex of $y = -3(x + 1)^2 + 4$?
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$(-1, 4)$.
$(-1, 4)$.
What is the vertex of $y = (x - 2)^2 + 5$?
What is the vertex of $y = (x - 2)^2 + 5$?
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$(2, 5)$.
$(2, 5)$.
Definition of a square root.
Definition of a square root.
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A number that, when multiplied by itself, equals the original number.
A number that, when multiplied by itself, equals the original number.
Domain of $f(x) = \sqrt{x - 5}$
Domain of $f(x) = \sqrt{x - 5}$
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$x \ge 5$.
$x \ge 5$.
Domain of $f(x) = \sqrt{x + 4}$.
Domain of $f(x) = \sqrt{x + 4}$.
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$x \ge -4$.
$x \ge -4$.
Explain why $\sqrt{-9}$ is not a real number.
Explain why $\sqrt{-9}$ is not a real number.
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No real number squared equals $-9$.
No real number squared equals $-9$.
For $y = -\sqrt{x}$, what happens to the graph?
For $y = -\sqrt{x}$, what happens to the graph?
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It reflects across the x-axis.
It reflects across the x-axis.
For $y = \sqrt{x - 4}$, what happens if 4 is increased?
For $y = \sqrt{x - 4}$, what happens if 4 is increased?
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Graph shifts right by 4.
Graph shifts right by 4.
For $y = 2\sqrt{x}$, what happens compared to $y = \sqrt{x}$?
For $y = 2\sqrt{x}$, what happens compared to $y = \sqrt{x}$?
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Graph is vertically stretched by factor of 2.
Graph is vertically stretched by factor of 2.
Given $f(x) = \sqrt{9 - x}$, what is the domain?
Given $f(x) = \sqrt{9 - x}$, what is the domain?
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$x \le 9$.
$x \le 9$.
Given $f(x) = \sqrt{x - 3}$, what is the domain?
Given $f(x) = \sqrt{x - 3}$, what is the domain?
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$x \ge 3$.
$x \ge 3$.
How does the absolute value of $a$ affect a parabola?
How does the absolute value of $a$ affect a parabola?
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Larger $|a|$ makes it narrower; smaller $|a|$ makes it wider.
Larger $|a|$ makes it narrower; smaller $|a|$ makes it wider.
If $f(x) = \sqrt{x - 1}$, what is the domain?
If $f(x) = \sqrt{x - 1}$, what is the domain?
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$x \ge 1$.
$x \ge 1$.
If $f(x) = \sqrt{x}$, what is $f(16)$?
If $f(x) = \sqrt{x}$, what is $f(16)$?
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4
4
Rationalize $\frac{3}{\sqrt{5}}$
Rationalize $\frac{3}{\sqrt{5}}$
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$\frac{3\sqrt{5}}{5}$.
$\frac{3\sqrt{5}}{5}$.
Simplify $(2\sqrt{3})(3\sqrt{2})$
Simplify $(2\sqrt{3})(3\sqrt{2})$
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$6\sqrt{6}$.
$6\sqrt{6}$.
Simplify $\sqrt[3]{27}$
Simplify $\sqrt[3]{27}$
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3
3
Simplify $\sqrt[3]{27}$.
Simplify $\sqrt[3]{27}$.
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3
3
Simplify $\sqrt{3x^2}$
Simplify $\sqrt{3x^2}$
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$|x|\sqrt{3}$.
$|x|\sqrt{3}$.
Simplify $\sqrt{49}$
Simplify $\sqrt{49}$
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7
7
Simplify $\sqrt{49}$.
Simplify $\sqrt{49}$.
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7
7
Simplify $\sqrt{50}$
Simplify $\sqrt{50}$
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$5\sqrt{2}$.
$5\sqrt{2}$.
Simplify $\sqrt{50}$.
Simplify $\sqrt{50}$.
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$5\sqrt{2}$.
$5\sqrt{2}$.
Simplify $\sqrt{72}$
Simplify $\sqrt{72}$
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$6\sqrt{2}$.
$6\sqrt{2}$.
Simplify $\sqrt{a^2}$
Simplify $\sqrt{a^2}$
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$|a|$.
$|a|$.
Simplify $\sqrt{x^4}$
Simplify $\sqrt{x^4}$
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$x^2$.
$x^2$.
Solve $\sqrt{x + 2} = x$
Solve $\sqrt{x + 2} = x$
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$x = 2$ (check eliminates $x = -1$).
$x = 2$ (check eliminates $x = -1$).
Solve $\sqrt{x} = 5$
Solve $\sqrt{x} = 5$
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$x = 25$.
$x = 25$.
Solve $\sqrt{x+3} = 4$
Solve $\sqrt{x+3} = 4$
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$x = 13$.
$x = 13$.
What is the definition of absolute value?
What is the definition of absolute value?
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Distance from 0 on a number line.
Distance from 0 on a number line.
Why must radical solutions be checked?
Why must radical solutions be checked?
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Squaring can introduce false solutions.
Squaring can introduce false solutions.