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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

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Example Questions

Example Question #241 : How To Find The Square Root

Solve:

$\sqrt{169}*\sqrt{144}$ $\displaystyle \sqrt{169}*\sqrt{144}$

Possible Answers:

272 $\displaystyle 272$

156 $\displaystyle 156$

$\displaystyle 25$

164 $\displaystyle 164$

140 $\displaystyle 140$

Correct answer:

156 $\displaystyle 156$

Explanation:

First find the individual square roots:

$\sqrt{169}=13$ $\displaystyle \sqrt{169}=13$

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

$\sqrt{169}*\sqrt{144}=13*12$ $\displaystyle \sqrt{169}*\sqrt{144}=13*12$

Then, multiply:

$\displaystyle 13*12=156$

Answer: 156 $\displaystyle 156$

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Example Question #242 : How To Find The Square Root

Solve:

$\sqrt{225}*\sqrt{100}$ $\displaystyle \sqrt{225}*\sqrt{100}$

Possible Answers:

125 $\displaystyle 125$

$\displaystyle 75$

150 $\displaystyle 150$

325 $\displaystyle 325$

132 $\displaystyle 132$

Correct answer:

150 $\displaystyle 150$

Explanation:

First, find the individual square roots:

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

$\sqrt{100}=10$ $\displaystyle \sqrt{100}=10$

$\sqrt{225}*\sqrt{100}=15*10$ $\displaystyle \sqrt{225}*\sqrt{100}=15*10$

Then, multiply:

$\displaystyle 15*10=150$

Answer: 150 $\displaystyle 150$

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Example Question #243 : How To Find The Square Root

Solve:

$\sqrt{121}+121$ $\displaystyle \sqrt{121}+121$

Possible Answers:

121 $\displaystyle 121$

$\displaystyle 11$

132 $\displaystyle 132$

$\displaystyle 99$

$\displaystyle 22$

Correct answer:

132 $\displaystyle 132$

Explanation:

First, find the square root:

$\sqrt{121}=11$ $\displaystyle \sqrt{121}=11$

$\sqrt{121}+121=11+121$ $\displaystyle \sqrt{121}+121=11+121$

Then, add:

$\displaystyle 11+121=132$

Answer: 132 $\displaystyle 132$

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Example Question #241 : Squares / Square Roots

Solve:

$89*\sqrt{36}=$ $\displaystyle 89*\sqrt{36}=$

Possible Answers:

None of these

354 $\displaystyle 354$

543 $\displaystyle 543$

435 $\displaystyle 435$

534 $\displaystyle 534$

Correct answer:

534 $\displaystyle 534$

Explanation:

First find the square root:

$\sqrt{36}=6$ $\displaystyle \sqrt{36}=6$

$89*\sqrt{36}=89*6$ $\displaystyle 89*\sqrt{36}=89*6$

Then multiply:

$\displaystyle 89*6=534$

Answer: 534 $\displaystyle 534$

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Example Question #245 : How To Find The Square Root

Solve:

$19*\sqrt{81}=$ $\displaystyle 19*\sqrt{81}=$

Possible Answers:

175 $\displaystyle 175$

181 $\displaystyle 181$

189 $\displaystyle 189$

171 $\displaystyle 171$

167 $\displaystyle 167$

Correct answer:

171 $\displaystyle 171$

Explanation:

First find the square root:

$\sqrt{81}=9$ $\displaystyle \sqrt{81}=9$

$19*\sqrt{81}=19*9$ $\displaystyle 19*\sqrt{81}=19*9$

Then multiply:

$\displaystyle 19*9=171$

Answer: 171 $\displaystyle 171$

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Example Question #246 : How To Find The Square Root

Solve:

$25*\sqrt{49}=$ $\displaystyle 25*\sqrt{49}=$

Possible Answers:

178 $\displaystyle 178$

175 $\displaystyle 175$

172 $\displaystyle 172$

170 $\displaystyle 170$

185 $\displaystyle 185$

Correct answer:

175 $\displaystyle 175$

Explanation:

First find the square root:

$\sqrt{49}=7$ $\displaystyle \sqrt{49}=7$

$25*\sqrt{49}=25*7$ $\displaystyle 25*\sqrt{49}=25*7$

Then multiply:

$\displaystyle 25*7=175$

Answer: 175 $\displaystyle 175$

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Example Question #247 : How To Find The Square Root

Solve:

$32*\sqrt{16}=$ $\displaystyle 32*\sqrt{16}=$

Possible Answers:

142 $\displaystyle 142$

130 $\displaystyle 130$

135 $\displaystyle 135$

126 $\displaystyle 126$

128 $\displaystyle 128$

Correct answer:

128 $\displaystyle 128$

Explanation:

First find the square root:

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

$32*\sqrt{16}=32*4$ $\displaystyle 32*\sqrt{16}=32*4$

Then multiply:

$\displaystyle 32*4=128$

Answer: 128 $\displaystyle 128$

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Example Question #248 : How To Find The Square Root

Solve for $\displaystyle a$.

$a^{2}=41+13-5$ $\displaystyle a^{2}=41+13-5$

Possible Answers:

$\displaystyle 7$

$\displaystyle 49$

$\frac{7}{2}$ $\displaystyle \frac{7}{2}$

$\frac{49}{2}$ $\displaystyle \frac{49}{2}$

$\displaystyle 6$

Correct answer:

$\displaystyle 7$

Explanation:

First, evaluate the right side of the equation.

$a^{2}=41+13-5$ $\displaystyle a^{2}=41+13-5$

$a^{2}=49$ $\displaystyle a^{2}=49$

Take the square root of both sides to solve for $\displaystyle a$.

$\sqrt{a^{2}}={\sqrt{49}}$ $\displaystyle \sqrt{a^{2}}={\sqrt{49}}$

a=7 $\displaystyle a=7$

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Example Question #242 : Squares / Square Roots

What is the square root of 75?

Possible Answers:

$5\sqrt{3}$ $\displaystyle 5\sqrt{3}$

$3\sqrt{5}$ $\displaystyle 3\sqrt{5}$

$\displaystyle 15$

$\displaystyle 23$

Correct answer:

$5\sqrt{3}$ $\displaystyle 5\sqrt{3}$

Explanation:

In order to take the square root of 75, we must first see whether there are any square numbers that are a factor of 75.

Given that 25 is both a square and a factor of 75, we would write the square root of 75 as:

$\sqrt{25\cdot 3}$ $\displaystyle \sqrt{25\cdot 3}$

This reduces to:

$5\sqrt{3}$ $\displaystyle 5\sqrt{3}$

That is therefore the correct answer.

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Example Question #243 : Squares / Square Roots

What is the square root of 169?

Possible Answers:

$\displaystyle 13$

13.5 $\displaystyle 13.5$

$\displaystyle 14$

$\displaystyle 15$

Correct answer:

$\displaystyle 13$

Explanation:

The square root of a number is a value that, when multiplied by itself, yields the number.

The easiest way to solve this problem is to multiply the answer choices by themselves until 169 is the product. Given that 13 times 13 is 169, 13 is the correct answer.

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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 #241 : How To Find The Square Root

Example Question #242 : How To Find The Square Root

Example Question #243 : How To Find The Square Root

Example Question #241 : Squares / Square Roots

Example Question #245 : How To Find The Square Root

Example Question #246 : How To Find The Square Root

Example Question #247 : How To Find The Square Root

Example Question #248 : How To Find The Square Root

Example Question #242 : Squares / Square Roots

Example Question #243 : Squares / Square Roots

All ISEE Middle Level Math Resources

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