How to divide square roots - SAT Math

Card 0 of 4

Question

(√27 + √12) / √3 is equal to

Answer

√27 is the same as 3√3, while √12 is the same as 2√3.

3√3 + 2√3 = 5√3

(5√3)/(√3) = 5

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Question

Simplify: $\frac{\sqrt{210}}{\sqrt{6}}$

Answer

When dividing square roots, we divide the numbers inside the radical. Simplify if necessary.

$\frac{\sqrt{210}}{\sqrt{6}}=\frac{\sqrt{35}*\sqrt{6}}{\sqrt{6}}=\sqrt{35}$

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Question

Simplify: $\frac{\sqrt{432}}{\sqrt{36}}$

Answer

When dividing square roots, we divide the numbers inside the radical. Simplify if necessary.

$\frac{\sqrt{432}}{\sqrt{36}}=\frac{\sqrt{36}\sqrt{12}}{\sqrt{36}}=\sqrt{12}$

Let's simplify this even further by factoring out a .

$\sqrt{12}=\sqrt{4}\sqrt{3}=2\sqrt{3}$

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Question

Simplify: $\frac{\sqrt{1200}}{\sqrt{8}}$

Answer

When dividing square roots, we divide the numbers inside the radical. Simplify if necessary.

$\frac{\sqrt{1200}}{\sqrt{8}}=\frac{\sqrt{8}\sqrt{150}}{\sqrt{8}}=\sqrt{150}$
Let's simplify this even further by factoring out a .

$\sqrt{150}=\sqrt{25}\sqrt{6}=5\sqrt{6}$

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