How to subtract square roots - PSAT Math

Card 0 of 2

Question

Evaluate: $\sqrt{108}-\sqrt{81}$

Answer

Let us factor 108 and 81

$108=2\times 54= 2\times 2\times 27= 2^2\times 3\times 9= 2^2\times 3^2\times 3$

$81=9\times 9=9^2$

$\sqrt{108}-\sqrt{81}=6\sqrt{3}-9$

Compare your answer with the correct one above

Question

$\sqrt{63}-\sqrt{28}$

Answer

Step one: Find the greatest square factor of each radical

For this is , and for it is .

Therefore:

$\sqrt{63}-\sqrt{28}=\sqrt{97}-\sqrt{47}$

Step two: Simplify the radicals

$\sqrt{97}-\sqrt{47}$

$3\sqrt{7}-2\sqrt{7}$

$\sqrt{7}$

Compare your answer with the correct one above

Tap the card to reveal the answer