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ISEE Middle Level Math : ISEE Middle Level (grades 7-8) Mathematics Achievement

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 #281 : Squares / Square Roots

Solve:

$\sqrt{144}\div 0=$ $\displaystyle \sqrt{144}\div 0=$

Possible Answers:

$\displaystyle 12$

$\displaystyle 0$

120 $\displaystyle 120$

undefined

144 $\displaystyle 144$

Correct answer:

undefined

Explanation:

Division of a non-zero number by 0 is always undefined. Therefore, there is no need to find the square root, because the answer will be undefined regardless of what number is under the square root sign.

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Example Question #282 : Squares / Square Roots

Solve:

$\sqrt{225}\div 3=$ $\displaystyle \sqrt{225}\div 3=$

Possible Answers:

$\displaystyle 15$

$\displaystyle 75$

$\displaystyle 3$

$\displaystyle 5$

Correct answer:

$\displaystyle 5$

Explanation:

First, find the square root:

$\sqrt{225}=15$ $\displaystyle \sqrt{225}=15$

Then complete the division:

$15\div 3=5$ $\displaystyle 15\div 3=5$

Answer: $\displaystyle 5$

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Example Question #283 : Squares / Square Roots

Solve the equation:

$\sqrt{16}*4=$ $\displaystyle \sqrt{16}*4=$

Possible Answers:

$\displaystyle 20$

$\displaystyle 16$

$\displaystyle 24$

$\displaystyle 19$

$\displaystyle 8$

Correct answer:

$\displaystyle 16$

Explanation:

First find the square root:

$\sqrt{16}=4$ $\displaystyle \sqrt{16}=4$

Then multiply:

4*4=16 $\displaystyle 4*4=16$

Answer: $\displaystyle 16$

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Example Question #284 : Squares / Square Roots

$\sqrt{144}*21=$ $\displaystyle \sqrt{144}*21=$

Possible Answers:

165 $\displaystyle 165$

225 $\displaystyle 225$

522 $\displaystyle 522$

252 $\displaystyle 252$

$\displaystyle 33$

Correct answer:

252 $\displaystyle 252$

Explanation:

First take the square root:

$\sqrt{144}=12$ $\displaystyle \sqrt{144}=12$

Then multiply:

$\displaystyle 12*21=252$

Answer: 252 $\displaystyle 252$

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Example Question #285 : Squares / Square Roots

$\sqrt{16}*660=$ $\displaystyle \sqrt{16}*660=$

Possible Answers:

2640 $\displaystyle 2640$

2046 $\displaystyle 2046$

2064 $\displaystyle 2064$

2460 $\displaystyle 2460$

Correct answer:

2640 $\displaystyle 2640$

Explanation:

First take the square root:

$\sqrt{16}=4$ $\displaystyle \sqrt{16}=4$

Then multiply:

$\displaystyle 4*660=2640$

Answer: 2640 $\displaystyle 2640$

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Example Question #286 : Squares / Square Roots

What is the simplified version of this expression:

$(4+3)^{2}$ $\displaystyle (4+3)^{2}$

Possible Answers:

$\displaystyle 49$

$\displaystyle 14$

$\displaystyle 27$

$\displaystyle 35$

Correct answer:

$\displaystyle 49$

Explanation:

The first step in solving this problem is to solve for the value in parentheses:

$(4+3)^{2}$ $\displaystyle (4+3)^{2}$

$7^{2}$ $\displaystyle 7^{2}$

This is equivalent to 7 times 7, which is 49. Therefore, 49 is the correct answer.

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Example Question #287 : Squares / Square Roots

What is the value of the following expression?

$(3-5)^{2}$ $\displaystyle (3-5)^{2}$

Possible Answers:

$\displaystyle -4$

$\displaystyle -2$

$\displaystyle 2$

$\displaystyle 4$

Correct answer:

$\displaystyle 4$

Explanation:

The first step in solving this problem is to solve for the value in parentheses:

$(3-5)^{2}$ $\displaystyle (3-5)^{2}$

$-2^{2}$ $\displaystyle -2^{2}$

Remember, a negative raised to an even power is positive. Therefore, 4 is the correct answer.

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Example Question #288 : Squares / Square Roots

Which of the values below is equal to $64\div {\sqrt{6-2}$ $\displaystyle 64\div {\sqrt{6-2}$?

Possible Answers:

$\displaystyle 36$

$\displaystyle 18$

$\displaystyle 32$

$\displaystyle 64$

Correct answer:

$\displaystyle 32$

Explanation:

$64\div {\sqrt{6-2}$ $\displaystyle 64\div {\sqrt{6-2}$ can be reduced to:

$64\div {\sqrt{4}$ $\displaystyle 64\div {\sqrt{4}$

$64\div 2$ $\displaystyle 64\div 2$

$\displaystyle 32$

Therefore, $\displaystyle 32$ is the correct answer.

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Example Question #289 : Squares / Square Roots

Simplify the following:

$\sqrt{169}$ $\displaystyle \sqrt{169}$

Possible Answers:

$\sqrt{169}$ $\displaystyle \sqrt{169}$

1.69 $\displaystyle 1.69$

$\pm14$ $\displaystyle \pm14$

$\pm13$ $\displaystyle \pm13$

Correct answer:

$\pm13$ $\displaystyle \pm13$

Explanation:

To solve, simply identify the number that when squared is equal to 169.

Recall that both negative and positive numbers when squared result in a positive number.

Thus,

$\sqrt{169}=\sqrt{13^2}=\pm13$ $\displaystyle \sqrt{169}=\sqrt{13^2}=\pm13$

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Example Question #290 : Squares / Square Roots

What is the side length of a square yard if the area of the yard is $\displaystyle 49$?

Possible Answers:

$\displaystyle 9$

$\displaystyle 10$

$\displaystyle 11$

$\displaystyle 25$

$\displaystyle 7$

Correct answer:

$\displaystyle 7$

Explanation:

The area of a square is the side length squared.

To find the side length from the area, you must find the square root of the area.

The square root whatever value multiplied by itself gives you your value.

$\displaystyle 7$ multiplied by itself gives you $\displaystyle 49$ so the side length must be $\displaystyle 7$.

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All ISEE Middle Level Math Resources

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ISEE Middle Level Math : ISEE Middle Level (grades 7-8) Mathematics Achievement

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

All ISEE Middle Level Math Resources

Example Questions

Example Question #281 : Squares / Square Roots

Example Question #282 : Squares / Square Roots

Example Question #283 : Squares / Square Roots

Example Question #284 : Squares / Square Roots

Example Question #285 : Squares / Square Roots

Example Question #286 : Squares / Square Roots

Example Question #287 : Squares / Square Roots

Example Question #288 : Squares / Square Roots

Example Question #289 : Squares / Square Roots

Example Question #290 : Squares / Square Roots

All ISEE Middle Level Math Resources

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