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ISEE Middle Level Math : Squares / Square Roots

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Example Questions

Example Question #121 : Squares / Square Roots

Find :

$\frac{\sqrt{x}+1}{\sqrt{x}-1}=2$

Possible Answers:

Correct answer:

Explanation:

$\frac{\sqrt{x}+1}{\sqrt{x}-1}=2\Rightarrow \sqrt{x}+1=2(\sqrt{x}-1)$

$\Rightarrow \sqrt{x}+1=2\sqrt{x}-2\Rightarrow 2\sqrt{x}-\sqrt{x}=1+2$

$\Rightarrow \sqrt{x}=3\Rightarrow x=3^2=9$

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Example Question #122 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Let $x=\sqrt{4^3-3^3}$ .

Which of the following statements is correct about ?

Possible Answers:

$5< \sqrt{37}< 6$

$7< \sqrt{37}< 8$

$4< \sqrt{37}< 5$

$8< \sqrt{37}< 9$

$6< \sqrt{37}< 7$

Correct answer:

$6< \sqrt{37}< 7$

Explanation:

$x=\sqrt{4^3-3^3}=\sqrt{64-27}=\sqrt{37}$

$36< 37< 49\Rightarrow \sqrt{36}< \sqrt{37}< \sqrt{49}$

$6< \sqrt{37}< 7$

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Example Question #121 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Simplify:

$\sqrt{108}$

Possible Answers:

$6\sqrt3$

$3\sqrt6$

$2\sqrt{54}$

$36\sqrt3$

Correct answer:

$6\sqrt3$

Explanation:

$\sqrt{108}=\sqrt{36}\times \sqrt3=6\times \sqrt3=6\sqrt3$

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Example Question #122 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Simplify:

$\sqrt{27x^3}$

Possible Answers:

$3x\sqrt3$

$3x\sqrt{x^2}$

$3\sqrt{3x^3}$

$3x\sqrt{3x}$

Correct answer:

$3x\sqrt{3x}$

Explanation:

$\sqrt{27x^3}=\sqrt{9x^2}\times \sqrt{3x}=3x\times \sqrt{3x}=3x\sqrt{3x}$

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Example Question #123 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Simplify:

$\sqrt{48}$

Possible Answers:

$4\sqrt{12}$

$2\sqrt{12}$

$4\sqrt3$

$16\sqrt3$

Correct answer:

$4\sqrt3$

Explanation:

$\sqrt{48}=\sqrt{16}\times \sqrt3=4\sqrt3$

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Example Question #124 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Simplify:

$\sqrt{72x^4}$

Possible Answers:

$6\sqrt{2x^4}$

$6x\sqrt{2x}$

$6x^2\sqrt2$

$6x^2\sqrt{2x}$

Correct answer:

$6x^2\sqrt2$

Explanation:

$\sqrt{72x^4}=\sqrt{72}\times \sqrt{x^4}=\sqrt{36}\times \sqrt{2}\times \sqrt{x^4}=6\times \sqrt2\times x^2$

$=6x^2\sqrt2$

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Example Question #125 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Evaluate $\sqrt{ 15 - x^{2} }$ for x = 8 .

Possible Answers:

$-\sqrt{79}$

The expression is undefined in the real numbers

Correct answer:

The expression is undefined in the real numbers

Explanation:

If x = 8 , then

$\sqrt{ 15 - x^{2} } = \sqrt{ 15 - 8^{2} } = \sqrt{ 15 - 64 } = \sqrt{ -49 }$ .

This is undefined in the real numbers, since negative numbers do not have real square roots.

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Example Question #126 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Evaluate $\sqrt{ 25 - x^{2} }$ for x = -4 .

Possible Answers:

The expression is undefined in the real numbers

$\sqrt{41}$

Correct answer:

Explanation:

If x = -4 , then $\sqrt{ 25 - x^{2} } = \sqrt{ 25 - (-4)^{2} } = \sqrt{ 25 - 16 } = \sqrt{ 9 } = 3$

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Example Question #127 : Isee Middle Level (Grades 7 8) Mathematics Achievement

$\sqrt{25}*\sqrt{36}=$

Possible Answers:

Correct answer:

Explanation:

Find the square root:

$\sqrt{25}=5$

$\sqrt{36}=6$

Solve the equation:

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Example Question #128 : Isee Middle Level (Grades 7 8) Mathematics Achievement

$\sqrt{144}*\sqrt{4}=$

Possible Answers:

148

Correct answer:

Explanation:

Find the square root:

$\sqrt{144}=12$

$\sqrt{4}=2$

Solve the equation: 12*2=24

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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 #121 : Squares / Square Roots

Example Question #122 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Example Question #121 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Example Question #122 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Example Question #123 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Example Question #124 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Example Question #125 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Example Question #126 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Example Question #127 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Example Question #128 : Isee Middle Level (Grades 7 8) Mathematics Achievement

All ISEE Middle Level Math Resources

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