How to subtract square roots

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PSAT Math › How to subtract square roots

Questions 1 - 2

1

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

$6\sqrt{3}-9$

$24\sqrt{3}-81$

$24\sqrt{3}-9$

$4\sqrt{27}-\sqrt{9}$

None of the available answers

Explanation

Let us factor 108 and 81

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

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

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

2

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

$\sqrt{7}$

$\sqrt{35}$

$5\sqrt{7}$

$\sqrt{5}$

$3\sqrt{11}$

Explanation

Step one: Find the greatest square factor of each radical

For this is , and for it is .

Therefore:

$\sqrt{63}-\sqrt{28}=\sqrt{9*7}-\sqrt{4*7}$

Step two: Simplify the radicals

$\sqrt{9*7}-\sqrt{4*7}$

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

$\sqrt{7}$

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