How to find the square root - ISEE Middle Level Math

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Question

$\dpi{100} (4+2)^{2}=$

Answer

Follow PEMDAS for order of operations. First, we add the numbers inside the parentheses.

$\dpi{100} 4+2=6$

Then we take $\dpi{100} 6^{2}=36$ .

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Question

$13.25 < \sqrt{x} < 13.5$

Which of the following is a possible value for ?

Answer

$13.25 < \sqrt{x} < 13.5$

We can find more information on the value of by squaring all of our terms to remove the square root.

$13.25^{2} < \left (\sqrt{x} \right )^{2}< 13.5^{2}$

Now we have a range of values for , however, none of these choices fall in this range.

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Question

What is the product of the square root of twice eighteen and four less than ten?

Answer

$\sqrt{218} (10-4)$

$\sqrt{36} *6$

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Question

Evaluate: $\sqrt{81} + \sqrt{25 } + \sqrt{36}$

Answer

Find the individual square roots and add them.

$\sqrt{81} = 9$

$\sqrt{25 } = 5$

$\sqrt{36} = 6$

$\sqrt{81} + \sqrt{25 } + \sqrt{36} = 9 + 5 + 6 = 20$

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Question

$\sqrt{81} \ast \left ( 33\div 11 \right )=$

Answer

First find the square root of $\sqrt{81}= 9$

Then solve what is inside the parentheses: $\left ( 33\div 11 \right )=3$

Solve the equation accordingly $9 \ast 3=27$

The answer is 27.

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Question

$\frac{\sqrt{9}+\sqrt{25}} \sqrt{4}$ =

Answer

First find the square root for each number. Then solve accordingly.

$\frac{3+5}{2}=\frac{8}{2}=4$

The answer is 4.

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Question

$\sqrt{25} + \sqrt{64} + \sqrt{16} =$

Answer

First, find the square root of each number, then add.

The answer is 17.

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Question

$3\sqrt{49} + \sqrt{144} =$

Answer

First, find the square roots of the numbers:

$\sqrt{49} = 7$

$\sqrt{144}=12$

Then, solve the equation using order of operations:

$3\left ( 7 \right ) + 12=$

The answer is .

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Question

$\frac{12\sqrt{121}}{\sqrt{16}}=$

Answer

First, find the square root for each number:

$\sqrt{121} = 11$

$\sqrt{16}=4$

Then, insert these square roots into the equation and solve accordingly:

$\frac{12\left ( 11 \right )}{4} =$

$\frac{132}{4}=33$

The answer is 33.

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Question

$4\left ( \sqrt{4} * \sqrt{9} \right )=$

Answer

First, find the square root for each:

$\sqrt{4}=2$

$\sqrt{9}=3$

Then insert these into the equation and solve:

$4 \left ( 2*3 \right )=$

The answer is

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Question

$\sqrt{81}\sqrt{25}\sqrt{49}=$

Answer

First, find the square root of each number:

$\sqrt{81 } = 9$

$\sqrt{25}=5$

$\sqrt{49}=7$

Solve the equation accordingly:

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Question

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

Answer

First find the square root of each number:

$\sqrt{49}=7$

$\sqrt{144}=12$

Then, solve accordingly:

The answer is 84.

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Question

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

Answer

First, find the square root for each number:

$\sqrt{64}=8$

$\sqrt{121}=11$

$\sqrt{36}=6$

Then, solve accordingly:

The answer is 528.

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Question

$\frac{\sqrt{169}*\sqrt{16}}{\sqrt{4}}=$

Answer

First, find the square root of each number:

$\sqrt{169}=13$

$\sqrt{16}=4$

$\sqrt{4}=2$

Then, solve accordingly:

$\frac{13*4}{2}=\frac{52}{2}=26$

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Question

Which of the following is true about $\sqrt{721}$ ?

Answer

$26^{2}=676 < 721 < 729 = 27^{2}$

so

$26=\sqrt{676} < \sqrt{721 }< \sqrt{729} = 27$

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Question

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

Answer

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

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

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

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

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Question

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

Answer

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

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Question

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

Answer

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 $\small 75\cdot 75=5625$ , our answer is $\small 75$ .

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Question

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

Answer

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

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

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Question

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

Answer

First, find the square root for each:

$\sqrt{25}=5$

$\sqrt{49}=7$

$\sqrt{16}=4$

Then, multiply:

Answer: 140.

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