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Algebra II : Non-Square Radicals

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Example Questions

Example Question #11 : Non Square Radicals

What is the value of $\sqrt{288}+\sqrt{48}$ ?

Possible Answers:

$12\sqrt3+4\sqrt2$

$12\sqrt2+4\sqrt3$

$12\sqrt2+3\sqrt2$

$16\sqrt6$

$16\sqrt5$

Correct answer:

$12\sqrt2+4\sqrt3$

Explanation:

Simplify the first term by using common factors of a perfect square.

$\sqrt{288} = \sqrt{144\times 2} = \sqrt{144} \cdot \sqrt{2} = 12\sqrt2$

Simplify the second term also by common factors.

$\sqrt{48} =\sqrt{4\cdot 4\cdot 3} =\sqrt{4}\cdot \sqrt{4}\cdot \sqrt{3} = 4\sqrt3$

Combine the terms.

$\sqrt{288}+\sqrt{48}=12\sqrt2+4\sqrt3$

The coefficients cannot be combined since these are unlike terms.

The answer is: $12\sqrt2+4\sqrt3$

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Example Question #11 : Non Square Radicals

Simplify: $\frac{\sqrt{32}}{\sqrt{6}}$

Possible Answers:

$\frac{\sqrt3}{4}$

$\frac{\sqrt3}{3}$

$\frac{\sqrt3}{2}$

$\frac{4\sqrt3}{3}$

$\frac{2\sqrt3}{3}$

Correct answer:

$\frac{4\sqrt3}{3}$

Explanation:

To simplify this, multiply the top and bottom by the denominator.

$\frac{\sqrt{32}}{\sqrt{6}}\cdot\frac{\sqrt{6}}{\sqrt{6}} = \frac{4\sqrt2\cdot \sqrt6}{6} =\frac{4\sqrt{12}}{6} =\frac{4\cdot 2\sqrt{3}}{6}$

Reduce the fraction.

The answer is: $\frac{4\sqrt3}{3}$

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Example Question #31 : Understanding Radicals

Simplify: $\sqrt{927}$

Possible Answers:

$3\sqrt{103}$

$103\sqrt{3}$

$9\sqrt{17}$

$12\sqrt{7}$

$9\sqrt{103}$

Correct answer:

$3\sqrt{103}$

Explanation:

To simplify radicals, we need to find perfect squares to factor out. In this case, it's .

$\sqrt{927}=\sqrt{9}*\sqrt{103}=3\sqrt{103}$ .

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Example Question #32 : Understanding Radicals

Simplify: $\sqrt{1248}$

Possible Answers:

$4\sqrt{78}$

$32\sqrt{39}$

$78\sqrt{14}$

$16\sqrt{13}$

$12\sqrt{78}$

Correct answer:

$4\sqrt{78}$

Explanation:

To simplify radicals, we need to find perfect squares to factor out. In this case, it's .

$\sqrt{1248}=\sqrt{16}*\sqrt{78}=4\sqrt{78}$

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Example Question #33 : Understanding Radicals

Simplify: $\sqrt{x^7y^3}$

Possible Answers:

$xy^2\sqrt{x^3y}$

$xy^2\sqrt{x^3y^2}$

$x^3y\sqrt{x^3y}$

$x^6y\sqrt{xy}$

$x^3y\sqrt{xy}$

Correct answer:

$x^3y\sqrt{xy}$

Explanation:

To simplify radicals, we need to find perfect squares to factor out. In this case, it's (x^3)^2,y^2 .

$\sqrt{x^7y^3}=\sqrt{x^6}*\sqrt{y^2}*\sqrt{xy}=\sqrt{(x^3)^2}*y\sqrt{xy}=x^3y\sqrt{xy}$

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Example Question #34 : Understanding Radicals

Simplify: $\sqrt{128x^4y^5}$

Possible Answers:

$64xy\sqrt{2xy}$

$8x^2y^2\sqrt{2xy}$

$64xy\sqrt{2y}$

$8x^2y^2\sqrt{2y}$

$8x^2y^2\sqrt{2x}$

Correct answer:

$8x^2y^2\sqrt{2y}$

Explanation:

To simplify radicals, we need to find perfect squares to factor out. In this case, it's 64,(x^2)^2, (y^2)^2 .

$\sqrt{128x^4y^5}=\sqrt{64}*\sqrt{(x^2)^2}*\sqrt{(y^2)^2}*\sqrt{2y}=8x^2y^2\sqrt{2y}$

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Example Question #35 : Radicals

Simplify: $2\sqrt{60} \cdot 3\sqrt{10}$

Possible Answers:

120

$60\sqrt6$

$24\sqrt{150}$

180

$30\sqrt6$

Correct answer:

$60\sqrt6$

Explanation:

Multiply the radicals.

$\sqrt{60} \times \sqrt{10} = \sqrt{600}$

Simplify this by writing the factors using perfect squares.

$\sqrt{600} = \sqrt{100} \times \sqrt{6} = 10\sqrt6$

Multiply this with the integers.

$2\sqrt{60} \cdot 3\sqrt{10} = 2\cdot 3 \cdot 10\sqrt6 = 60\sqrt6$

The answer is: $60\sqrt6$

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Example Question #3941 : Algebra Ii

Simplify: $10\sqrt{20}\cdot 30\sqrt{40}$

Possible Answers:

$6000\sqrt2$

$40+2\sqrt{10} +2\sqrt5$

$800\sqrt6$

$3000\sqrt2$

$20\sqrt{5}+60\sqrt{10}$

Correct answer:

$6000\sqrt2$

Explanation:

Multiply the integers and combine the radicals together by multiplication.

$10\sqrt{20}\cdot 30\sqrt{40} =300 \sqrt{800}$

Break up square root of 800 by common factors of perfect squares.

$300 \sqrt{800} = 300 \times \sqrt{100}\times \sqrt{4}\times \sqrt2$

Simplify the possible radicals.

$300\times 10 \times 2 \times \sqrt2 = 6000\sqrt2$

The answer is: $6000\sqrt2$

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Example Question #18 : Non Square Radicals

Evaluate: $5\sqrt{30}\cdot 4\sqrt{10}$

Possible Answers:

260

$200\sqrt3$

$20\sqrt{30}$

$200\sqrt6$

$6\sqrt5$

Correct answer:

$200\sqrt3$

Explanation:

Multiply the integers and the value of the square roots to combine as one radical.

$5\sqrt{30}\cdot 4\sqrt{10} = 20\sqrt{300}$

Simplify the radical. Use factors of perfect squares to simplify root 300.

$20\sqrt{300} = 20 \sqrt{100} \cdot \sqrt{3}= 20\cdot 10\cdot \sqrt3$

The answer is: $200\sqrt3$

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Example Question #41 : Understanding Radicals

Simplify: $12\sqrt{56}$

Possible Answers:

$48\sqrt{7}$

$29\sqrt5$

$24\sqrt{14}$

$\textup{This radical is already simplified.}$

$56\sqrt3$

Correct answer:

$24\sqrt{14}$

Explanation:

In order to simplify the radical, we will need to pull out common factors of possible perfect squares.

$12\sqrt{56} = 12\cdot \sqrt{8}\cdot \sqrt{7}=12\cdot \sqrt{4}\cdot \sqrt{2}\cdot \sqrt{7}$

The expression becomes:

$12\cdot 2\cdot \sqrt{2}\cdot \sqrt{7} = 24\sqrt{14}$

The radical 14 does not have any common factors of perfect squares.

The answer is: $24\sqrt{14}$

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Algebra II : Non-Square Radicals

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #11 : Non Square Radicals

Example Question #11 : Non Square Radicals

Example Question #31 : Understanding Radicals

Example Question #32 : Understanding Radicals

Example Question #33 : Understanding Radicals

Example Question #34 : Understanding Radicals

Example Question #35 : Radicals

Example Question #3941 : Algebra Ii

Example Question #18 : Non Square Radicals

Example Question #41 : Understanding Radicals

All Algebra II Resources

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