SAT Math : How to subtract square roots

Study concepts, example questions & explanations for SAT Math

varsity tutors app store varsity tutors android store varsity tutors ibooks store

Example Questions

Example Question #1731 : Psat Mathematics

Evaluate: \(\displaystyle \sqrt{108}-\sqrt{81}\)

Possible Answers:

\(\displaystyle 6\sqrt{3}-9\)

\(\displaystyle 24\sqrt{3}-9\)

None of the available answers

\(\displaystyle 24\sqrt{3}-81\)

\(\displaystyle 4\sqrt{27}-\sqrt{9}\)

Correct answer:

\(\displaystyle 6\sqrt{3}-9\)

Explanation:

Let us factor 108 and 81

\(\displaystyle 108=2\times 54= 2\times 2\times 27= 2^2\times 3\times 9= 2^2\times 3^2\times 3\)

\(\displaystyle 81=9\times 9=9^2\)

\(\displaystyle \sqrt{108}-\sqrt{81}=6\sqrt{3}-9\)

Learning Tools by Varsity Tutors