SAT Math : How to simplify square roots

Study concepts, example questions & explanations for SAT Math

varsity tutors app store varsity tutors android store

Example Questions

← Previous 1 3 4 5 6

Example Question #1 : Simplifying Square Roots

Simplify

÷ √3

Possible Answers:

not possible

3√3

none of these

2

3

Correct answer:

3√3

Explanation:

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

Asatsimplifysquare_root

Example Question #5 : How To Simplify Square Roots

Simplify:

√112

Possible Answers:

12

4√7

10√12

20

4√10

Correct answer:

4√7

Explanation:

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

Example Question #3 : Factoring And Simplifying Square Roots

Simplify:

 

√192

Possible Answers:
8√3
4√2
4√3
8√2
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

Example Question #3 : Simplifying Square Roots

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

Possible Answers:

12\sqrt{27}

144\sqrt{27}

2\sqrt{972}

2304\sqrt{2}

Correct answer:

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

Example Question #1 : How To Simplify Square Roots

Simplify:

 

Possible Answers:

Correct answer:

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

Example Question #1 : How To Simplify Square Roots

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

Possible Answers:

3√(2)

1

None of the other answers

√(2) + 1

√(3)

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

Example Question #13 : Simplifying Square Roots

what is 

√0.0000490

Possible Answers:

49

0.07

0.00007

0.007

7

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

Example Question #14 : Simplifying Square Roots

Simplify:

Possible Answers:

Correct answer:

Explanation:

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

Example Question #14 : Simplifying Square Roots

Simplify (\frac{16}{81})^{1/4}.

Possible Answers:

\frac{2}{3}

\frac{8}{81}

\frac{2}{81}

\frac{4}{9}

\frac{4}{81}

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}

Example Question #1 : How To Simplify Square Roots

Simplfy the following radical .

Possible Answers:

Correct answer:

Explanation:

You can rewrite the equation as .

This simplifies to .

← Previous 1 3 4 5 6
Learning Tools by Varsity Tutors

Incompatible Browser

Please upgrade or download one of the following browsers to use Instant Tutoring: