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SAT Math : How to simplify square roots

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Example Questions

Example Question #1 : Simplifying Square Roots

Simplify

9 ÷ √3

Possible Answers:

not possible

3√3

none of these

Correct answer:

3√3

Explanation:

in order to simplify a square root on the bottom, multiply top and bottom by the root

Asatsimplifysquare_root

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Example Question #2 : Simplifying Square Roots

Simplify:

√112

Possible Answers:

4√7

10√12

4√10

Correct answer:

4√7

Explanation:

√112 = {√2 * √56} = {√2 * √2 * √28} = {2√28} = {2√4 * √7} = 4√7

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Example Question #31 : Basic Squaring / Square Roots

Simplify:

√192

Possible Answers:

4√2

8√2

4√3

8√3

None of these

Correct answer: 8√3

Explanation:

√192 = √2 X √96

√96 = √2 X √48

√48 = √4 X√12

√12 = √4 X √3

√192 = √(2X2X4X4) X √3

= √4X√4X√4 X √3

= 8√3

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Example Question #1 : How To Simplify Square Roots

What is the simplest way to express $\sqrt{3888}$ ?

Possible Answers:

$2304\sqrt{2}$

$144\sqrt{27}$

$2\sqrt{972}$

$12\sqrt{27}$

$36\sqrt{3}$

Correct answer:

$36\sqrt{3}$

Explanation:

First we will list the factors of 3888:

$3888=3\times1296=3\times\3\times432=3^2\times12\times36=3^2\times12\times12\times3=3^2\times12^2\times3$

$\sqrt{3888}=\sqrt{3^{2}\times 12^{2}\times 3}=\sqrt{3^{2}}\times\sqrt{12^{2}} \times \sqrt{3}=3\times 12\times \sqrt{3}=36\sqrt{3}$

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Example Question #1 : How To Simplify Square Roots

Simplify:

$4\sqrt{27}+16\sqrt{75}+3\sqrt{12}$

Possible Answers:

$92\sqrt{3}$

$80\sqrt{3}$

$98\sqrt{3}$

$96\sqrt{3}$

$16\sqrt{3}$

Correct answer:

$98\sqrt{3}$

Explanation:

4√27 + 16√75 +3√12 =

4*(√3)*(√9) + 16*(√3)*(√25) +3*(√3)*(√4) =

4*(√3)*(3) + 16*(√3)*(5) + 3*(√3)*(2) =

12√3 + 80√3 +6√3= 98√3

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Example Question #11 : Simplifying Square Roots

Simplify the following: (√(6) + √(3)) / √(3)

Possible Answers:

√(2) + 1

3√(2)

√(3)

None of the other answers

Correct answer:

√(2) + 1

Explanation:

Begin by multiplying top and bottom by √(3):

(√(18) + √(9)) / 3

Note the following:

√(9) = 3

√(18) = √(9 * 2) = √(9) * √(2) = 3 * √(2)

Therefore, the numerator is: 3 * √(2) + 3. Factor out the common 3: 3 * (√(2) + 1)

Rewrite the whole fraction:

(3 * (√(2) + 1)) / 3

Simplfy by dividing cancelling the 3 common to numerator and denominator: √(2) + 1

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Example Question #601 : Gre Quantitative Reasoning

what is

√0.0000490

Possible Answers:

0.007

0.00007

0.07

Correct answer:

0.007

Explanation:

easiest way to simplify: turn into scientific notation

√0.0000490= √4.9 X 10^-5

finding the square root of an even exponent is easy, and 49 is a perfect square, so we can write out an improper scientific notation:

√4.9 X 10^-5 = √49 X 10^-6

√49 = 7; √10^-6 = 10^-3 this is equivalent to raising 10^-6 to the 1/2 power, in which case all that needs to be done is multiply the two exponents: 7 X 10^-3= 0.007

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Example Question #3 : How To Simplify Square Roots

Simplify: $\sqrt{576}$

Possible Answers:

$10\sqrt{12}$

$12\sqrt{6}$

$12\sqrt{3}$

Correct answer:

Explanation:

In order to take the square root, divide 576 by 2.

$\dpi{100} \sqrt{576}= \sqrt{2}\sqrt{288}=\sqrt{2}\sqrt{2}\sqrt{144}=\sqrt{4}\sqrt{144}=2\cdot 12=24$

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Example Question #111 : Arithmetic

Simplify $(\frac{16}{81})^{1/4}$ .

Possible Answers:

$\frac{8}{81}$

$\frac{2}{81}$

$\frac{2}{3}$

$\frac{4}{81}$

$\frac{4}{9}$

Correct answer:

$\frac{2}{3}$

Explanation:

$(\frac{16}{81})^{1/4}$

$\frac{16^{1/4}}{81^{1/4}}$

$\frac{(2\cdot 2\cdot 2\cdot 2)^{1/4}}{(3\cdot 3\cdot 3\cdot 3)^{1/4}}$

$\frac{2}{3}$

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Example Question #5 : How To Simplify Square Roots

Simplfy the following radical $\sqrt{20x^{2}}$ .

Possible Answers:

$2\sqrt{5x^{2}}$

$4\sqrt{5x}$

$2x\sqrt{10}$

$2x\sqrt{5}$

Correct answer:

$2x\sqrt{5}$

Explanation:

You can rewrite the equation as $\sqrt{20x^2}=(x)\sqrt{5} \cdot \sqrt{4}$ .

This simplifies to $2x\sqrt{5}$ .

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SAT Math : How to simplify square roots

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #1 : Simplifying Square Roots

Example Question #2 : Simplifying Square Roots

Example Question #31 : Basic Squaring / Square Roots

Example Question #1 : How To Simplify Square Roots

Example Question #1 : How To Simplify Square Roots

Example Question #11 : Simplifying Square Roots

Example Question #601 : Gre Quantitative Reasoning

Example Question #3 : How To Simplify Square Roots

Example Question #111 : Arithmetic

Example Question #5 : How To Simplify Square Roots

All SAT Math Resources

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