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ISEE Middle Level Math : Squares / Square Roots

Study concepts, example questions & explanations for ISEE Middle Level Math

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All ISEE Middle Level Math Resources

6 Diagnostic Tests 303 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #301 : Squares / Square Roots

Solve:

$\sqrt{324}$

Possible Answers:

Correct answer:

Explanation:

$\sqrt{324} = 18$

because $18 \times 18 = 324$

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Example Question #302 : Squares / Square Roots

Solve:

$-\sqrt{100}$

Possible Answers:

Correct answer:

Explanation:

$-\sqrt{100}$ indicates the negative square root of 100. .

The square root of 100 =10 because $10 \times 10 = 100.$

Because the negative sign is outside of the radical sign

$-\sqrt{100} = -10$

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Example Question #303 : Squares / Square Roots

$Solve: \frac{\sqrt{256}- \sqrt{169}}{\sqrt{16}} =$

Possible Answers:

$\frac{3}{4}$

$\frac{1}{4}$

$\frac{4}{3}$

Correct answer:

$\frac{3}{4}$

Explanation:

$\sqrt{256} = 16$

$\sqrt{169} =13$

$\sqrt{16} = 4$

$\frac{16-13}{4} = \frac{3}{4}$

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Example Question #304 : Squares / Square Roots

What is the $\sqrt{10}$ rounded to the nearest hundreth?

Possible Answers:

3.75

3.91

3.63

3.16

Correct answer:

3.16

Explanation:

To find the $\sqrt{10}$ , find the two perfect squares that this is between.

$\sqrt{9}$ and the $\sqrt{16}$ would be the two perfect squares. Recall that square roots come from either two positive values multiplied together or two negative numbers are multiplied together. Thus two separate equations will need to be used to calculate the possible value of $\sqrt{10}$ .

Let's first take a look at the perfect square which surround $\sqrt{10}$ .

$\sqrt{9} = \pm3\Rightarrow(-3)(-3)=9; (3)(3)=9$

$\sqrt{16} = \pm4 \Rightarrow (-4)(-4)=16;(4)(4)=16$

In this particular case $\sqrt{10$ would be closer to the $\sqrt{9}$ then the $\sqrt{16}$ because 10 is closer to 9 thus the appropriate estimation would be,

$\sqrt{10} = 3.16$ .

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Example Question #305 : Squares / Square Roots

Estimate $y^{2} =40$ to the nearest whole integer.

Possible Answers:

$y=\pm7$

$y=\pm6$

$y=\pm20$

$y=\pm 8$

Correct answer:

$y=\pm6$

Explanation:

$y^{2} =40$

Take the square root of both sides of the equation.

$\sqrt{y^{2}} = \sqrt{40}$

The first perfect square that is less than is 36.

The first perfect square that is greater than is 49.

$\sqrt{36} < \sqrt{40} < \sqrt{49}$

$6< \sqrt{40} < 7$

The $\sqrt{40}$ ls between and

is closer to than .

For the equation there are 2 solutions, because is positive: $y=\sqrt{a}$ , which is positive, and $y = -\sqrt{a}$ , which is negative. Together, these two roots are denoted $\pm\sqrt{a}$ .

$6 \times 6 = 36$

$-6 \times -6 = 36$

y = 6 or y = -6

$y=\pm6$ is the correct answer.

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Example Question #305 : Squares / Square Roots

$-\sqrt{\frac{16}{49}}$

Possible Answers:

$-\frac{7}{4}$

$\pm\frac{4}{7}$

$-\frac{4}{7}$

$\frac{4}{7}$

Correct answer:

$-\frac{4}{7}$

Explanation:

$-\sqrt{\frac{16}{49}}$

$\sqrt{16} = 4$ because $4\times4 =16$ .

$\sqrt{49} = 7$ because $7 \times 7 = 49.$

The negative sign outside the radical sign indicates that you are taking the negative square root of what is inside the radical sign, or the radicand.

$-\frac{4}{7}$ is the correct answer.

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Example Question #306 : Squares / Square Roots

If the area of a pasture is $144\textup{ ft}^{2}$ , and the pasture is a square, what is the length of one side of the pasture?

Possible Answers:

$11\textup{ ft}$

$14\textup{ ft}$

$13\textup{ ft}$

$12\textup{ ft}$

Correct answer:

$12\textup{ ft}$

Explanation:

The area of a square is the side length squared. To find the side length of the square, find the

$\sqrt{144}$ or what number times itself gives 144 as the product.

$\sqrt{144} = 12$ because $12 \times 12 = 144$

The correct answer is ft.

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Example Question #307 : Squares / Square Roots

Solve the equation:

$b^{2} =\frac{9}{441}$

Possible Answers:

$b = \pm \frac{3}{20}$

$b =\pm \frac{1}{21}$

$b = \pm\frac{1}{7}$

$b = \pm7$

Correct answer:

$b = \pm\frac{1}{7}$

Explanation:

$b^{2} =\frac{9}{441}$

Take the square root of both sides of the equation:

$\sqrt{b^{2}} =\sqrt{\frac{9}{441}}$

For the equation $\sqrt{b^{2}} =\sqrt{\frac{9}{441}}$ there are 2 solutions, because it is positive: $y=\sqrt{a}$ , which is positive, and $y = -\sqrt{a}$ , which is negative. Together, these two roots are denoted $\pm\sqrt{a}$ .

$3\times3 = 9$

$-3 \times -3 = 9$

$-21\times-21 =441$

$21\times21 = 441$

$b = \frac{3}{21} or -\frac{3}{21}$

$b=\pm\frac{1}{7}$

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Example Question #308 : Squares / Square Roots

Determine the value of the square root: $\sqrt{529}$

Possible Answers:

Correct answer:

Explanation:

The square root of a number determines one number that multiplies by itself to get the number inside the square root.

Notice that the number in the radical ends with a 9. This means the ones digit of the final answer must be three.

The answers and cannot be true since:

20^2 = 400

30^2 =900

Those values are far too small to be the correct answer.

The only possible answer is .

The answer is:

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All ISEE Middle Level Math Resources

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ISEE Middle Level Math : Squares / Square Roots

Study concepts, example questions & explanations for ISEE Middle Level Math

All ISEE Middle Level Math Resources

Example Questions

Example Question #301 : Squares / Square Roots

Example Question #302 : Squares / Square Roots

Example Question #303 : Squares / Square Roots

Example Question #304 : Squares / Square Roots

Example Question #305 : Squares / Square Roots

Example Question #305 : Squares / Square Roots

Example Question #306 : Squares / Square Roots

Example Question #307 : Squares / Square Roots

Example Question #308 : Squares / Square Roots

All ISEE Middle Level Math Resources

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