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ISEE Middle Level Math : How to find the square root

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 #11 : How To Find The Square Root

$\sqrt{49}\ast \sqrt{144}=$ $\displaystyle \sqrt{49}\ast \sqrt{144}=$

Possible Answers:

$\displaystyle 5$

$\displaystyle 19$

193 $\displaystyle 193$

$\displaystyle 84$

Correct answer:

$\displaystyle 84$

Explanation:

First find the square root of each number:

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

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

Then, solve accordingly:

7*12=84 $\displaystyle 7*12=84$

The answer is 84.

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Example Question #12 : How To Find The Square Root

$\sqrt{64}*\sqrt{121}*\sqrt{36}=$ $\displaystyle \sqrt{64}*\sqrt{121}*\sqrt{36}=$

Possible Answers:

221 $\displaystyle 221$

176 $\displaystyle 176$

528 $\displaystyle 528$

$\displaystyle 74$

Correct answer:

528 $\displaystyle 528$

Explanation:

First, find the square root for each number:

$\sqrt{64}=8$ $\displaystyle \sqrt{64}=8$

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

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

Then, solve accordingly:

$\displaystyle 8*11*6=528$

The answer is 528.

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Example Question #13 : Squares / Square Roots

Evaluate: $\sqrt{576} + \sqrt{196}$ $\displaystyle \sqrt{576} + \sqrt{196}$

Possible Answers:

$\displaystyle 42$

$\displaystyle 40$

$\displaystyle 38$

$\displaystyle 48$

$\displaystyle 28$

Correct answer:

$\displaystyle 38$

Explanation:

The square root of a number is the number which, when squared (multiplied by itself), yields that number.

$24 \cdot 24 = 576$ $\displaystyle 24 \cdot 24 = 576$ , so $\sqrt{ 576} = 24$ $\displaystyle \sqrt{ 576} = 24$

$14 \cdot 14 =196$ $\displaystyle 14 \cdot 14 =196$ , so $\sqrt{196 }= 14$ $\displaystyle \sqrt{196 }= 14$

$\sqrt{ 576} + \sqrt{196 } = 24 + 14 = 38$ $\displaystyle \sqrt{ 576} + \sqrt{196 } = 24 + 14 = 38$

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Example Question #14 : Squares / Square Roots

Evaluate: $\sqrt{-9} + \sqrt{16}$ $\displaystyle \sqrt{-9} + \sqrt{16}$

Possible Answers:

$\displaystyle -7$

$\displaystyle 1$

$\displaystyle 7$

$\sqrt{-9} + \sqrt{16}$ $\displaystyle \sqrt{-9} + \sqrt{16}$ is undefined in the set of real numbers.

$\displaystyle -1$

Correct answer:

$\sqrt{-9} + \sqrt{16}$ $\displaystyle \sqrt{-9} + \sqrt{16}$ is undefined in the set of real numbers.

Explanation:

Since negative numbers do not have square roots in the real number system, $\sqrt{-9}$ $\displaystyle \sqrt{-9}$ is undefined - and, subsequently, so is $\sqrt{-9} + \sqrt{16}$ $\displaystyle \sqrt{-9} + \sqrt{16}$ - in the set of real numbers.

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Example Question #13 : How To Find The Square Root

$\sqrt{25}*\sqrt{49}*\sqrt{16}=$ $\displaystyle \sqrt{25}*\sqrt{49}*\sqrt{16}=$

Possible Answers:

140 $\displaystyle 140$

105 $\displaystyle 105$

120 $\displaystyle 120$

$\displaystyle 90$

Correct answer:

140 $\displaystyle 140$

Explanation:

First, find the square root for each:

$\sqrt{25}=5$ $\displaystyle \sqrt{25}=5$

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

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

Then, multiply: $\displaystyle 5*7*4=140$

Answer: 140.

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Example Question #14 : How To Find The Square Root

What is the square root of $\small 5625$ $\displaystyle \small 5625$ ?

Possible Answers:

$\small 65$ $\displaystyle \small 65$

$\small 76$ $\displaystyle \small 76$

$\small 74$ $\displaystyle \small 74$

$\small 75$ $\displaystyle \small 75$

$\displaystyle 85$

Correct answer:

$\small 75$ $\displaystyle \small 75$

Explanation:

In order to find the square root of 5625, we must find a number that when multiplied by itself, gives a product of 5625. Since $\small 75\cdot 75=5625$ $\displaystyle \small 75\cdot 75=5625$ , our answer is $\small 75$ $\displaystyle \small 75$ .

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Example Question #17 : Squares / Square Roots

What is the square root of the sum of $\small 25$ $\displaystyle \small 25$ and $\small 75$ $\displaystyle \small 75$ ?

Possible Answers:

$\small 20$ $\displaystyle \small 20$

$\small 15$ $\displaystyle \small 15$

$\small 12$ $\displaystyle \small 12$

$\small 11$ $\displaystyle \small 11$

$\small 10$ $\displaystyle \small 10$

Correct answer:

$\small 10$ $\displaystyle \small 10$

Explanation:

In order to find the square root of the sum of $\small 25$ $\displaystyle \small 25$ and $\small 75$ $\displaystyle \small 75$ , we must first find the sum by adding them together. $\small 25+75=100$ $\displaystyle \small 25+75=100$

Next we must find a number that when multiplied by itself yields a product of 100. Since $\small 10\cdot 10=100$ $\displaystyle \small 10\cdot 10=100$ , our answer is $\displaystyle 10$ .

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Example Question #15 : How To Find The Square Root

$\frac{\sqrt{121}*5}{\sqrt{25}}=$ $\displaystyle \frac{\sqrt{121}*5}{\sqrt{25}}=$

Possible Answers:

$\displaystyle 5$

$\displaystyle 11$

$\displaystyle 55$

$\displaystyle 25$

Correct answer:

$\displaystyle 11$

Explanation:

First, find the square roots:

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

$\sqrt{25}=5$ $\displaystyle \sqrt{25}=5$

Then, solve accordingly:

$\frac{11*5}{5}=\frac{55}{5}=11$ $\displaystyle \frac{11*5}{5}=\frac{55}{5}=11$

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Example Question #16 : How To Find The Square Root

$\sqrt{81}*\sqrt{49} *\sqrt{4}=$ $\displaystyle \sqrt{81}*\sqrt{49} *\sqrt{4}=$

Possible Answers:

126 $\displaystyle 126$

100 $\displaystyle 100$

120 $\displaystyle 120$

110 $\displaystyle 110$

Correct answer:

126 $\displaystyle 126$

Explanation:

FIrst, find the square roots:

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

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

$\sqrt{4}=2$ $\displaystyle \sqrt{4}=2$

Then solve accordingly:

$\displaystyle 9*7*2=126$

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Example Question #17 : How To Find The Square Root

$\sqrt{64}\div \sqrt{16}=$ $\displaystyle \sqrt{64}\div \sqrt{16}=$

Possible Answers:

$\displaystyle 2$

$\displaystyle 6$

$\displaystyle 8$

$\displaystyle 4$

Correct answer:

$\displaystyle 2$

Explanation:

First, solve the square roots:

$\sqrt{64}=8$ $\displaystyle \sqrt{64}=8$

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

Then, solve accordingly:

$8\div 4=2$ $\displaystyle 8\div 4=2$

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All ISEE Middle Level Math Resources

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ISEE Middle Level Math : How to find the square root

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

All ISEE Middle Level Math Resources

Example Questions

Example Question #11 : How To Find The Square Root

Example Question #12 : How To Find The Square Root

Example Question #13 : Squares / Square Roots

Example Question #14 : Squares / Square Roots

Example Question #13 : How To Find The Square Root

Example Question #14 : How To Find The Square Root

Example Question #17 : Squares / Square Roots

Example Question #15 : How To Find The Square Root

Example Question #16 : How To Find The Square Root

Example Question #17 : How To Find The Square Root

All ISEE Middle Level Math Resources

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