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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 #1 : Isee Middle Level (Grades 7 8) Mathematics Achievement

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

Possible Answers:

$\dpi{100} 36$ $\displaystyle \dpi{100} 36$

$\dpi{100} 4$ $\displaystyle \dpi{100} 4$

$\dpi{100} 16$ $\displaystyle \dpi{100} 16$

$\dpi{100} 6$ $\displaystyle \dpi{100} 6$

Correct answer:

$\dpi{100} 36$ $\displaystyle \dpi{100} 36$

Explanation:

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

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

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

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Example Question #1 : How To Find The Square Root

$13.25 < \sqrt{x} < 13.5$ $\displaystyle 13.25 < \sqrt{x} < 13.5$

Which of the following is a possible value for $\displaystyle x$?

Possible Answers:

185 $\displaystyle 185$

183 $\displaystyle 183$

175 $\displaystyle 175$

169 $\displaystyle 169$

None of the other answers are correct.

Correct answer:

None of the other answers are correct.

Explanation:

$13.25 < \sqrt{x} < 13.5$ $\displaystyle 13.25 < \sqrt{x} < 13.5$

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

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

175.5625<x< 182.25 $\displaystyle 175.5625< x< 182.25$

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

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Example Question #1 : How To Find The Square Root

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

Possible Answers:

$\displaystyle 16$

$\displaystyle 17$

$\displaystyle 18$

$\displaystyle 20$

$\displaystyle 22$

Correct answer:

$\displaystyle 20$

Explanation:

Find the individual square roots and add them.

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

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

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

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

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Example Question #1 : Isee Middle Level (Grades 7 8) Mathematics Achievement

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

Possible Answers:

$\displaystyle 6$

$\displaystyle 60$

$\displaystyle 54$

$\displaystyle 24$

$\displaystyle 36$

Correct answer:

$\displaystyle 36$

Explanation:

$\sqrt{2*18} *(10-4)$ $\displaystyle \sqrt{2*18} *(10-4)$

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

6*6=36 $\displaystyle 6*6=36$

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Example Question #2 : Isee Middle Level (Grades 7 8) Mathematics Achievement

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

Possible Answers:

$\displaystyle 2$

$\displaystyle 4$

$\displaystyle 8$

$\displaystyle 6$

Correct answer:

$\displaystyle 4$

Explanation:

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

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

The answer is 4.

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Example Question #1 : Isee Middle Level (Grades 7 8) Mathematics Achievement

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

Possible Answers:

$\displaystyle 3$

$\displaystyle 25$

$\displaystyle 17$

$\displaystyle 13$

Correct answer:

$\displaystyle 17$

Explanation:

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

$\displaystyle 5 + 8 + 4=$

$\displaystyle 17$

The answer is 17.

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Example Question #1 : Isee Middle Level (Grades 7 8) Mathematics Achievement

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

Possible Answers:

$\displaystyle 2$

$\displaystyle 22$

$\displaystyle 33$

252 $\displaystyle 252$

333 $\displaystyle 333$

Correct answer:

$\displaystyle 33$

Explanation:

First, find the square roots of the numbers:

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

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

Then, solve the equation using order of operations:

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

$\displaystyle 21 + 12 = 33$

The answer is $\displaystyle 33$.

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Example Question #8 : Squares / Square Roots

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

Possible Answers:

$\displaystyle 20$

$\displaystyle 17$

$\displaystyle 24$

$\displaystyle 52$

Correct answer:

$\displaystyle 24$

Explanation:

First, find the square root for each:

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

$\sqrt{9}=3$ $\displaystyle \sqrt{9}=3$

Then insert these into the equation and solve:

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

4*6=24 $\displaystyle 4*6=24$

The answer is 24. $\displaystyle 24.$

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Example Question #5 : How To Find The Square Root

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

Possible Answers:

$\displaystyle 12$

$\displaystyle 33$

$\displaystyle 42$

$\displaystyle 8$

Correct answer:

$\displaystyle 33$

Explanation:

First, find the square root for each number:

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

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

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

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

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

The answer is 33.

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Example Question #2 : Isee Middle Level (Grades 7 8) Mathematics Achievement

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

Possible Answers:

$\displaystyle 21$

155 $\displaystyle 155$

$\displaystyle 52$

315 $\displaystyle 315$

Correct answer:

315 $\displaystyle 315$

Explanation:

First, find the square root of each number:

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

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

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

Solve the equation accordingly:

$\displaystyle 9*5*7=315$

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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 #1 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Example Question #1 : How To Find The Square Root

Example Question #1 : How To Find The Square Root

Example Question #1 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Example Question #2 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Example Question #1 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Example Question #1 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Example Question #8 : Squares / Square Roots

Example Question #5 : How To Find The Square Root

Example Question #2 : Isee Middle Level (Grades 7 8) Mathematics Achievement

All ISEE Middle Level Math Resources

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