How to divide square roots - PSAT Math

Card 0 of 5

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

Divide and simplify. Assume all integers are positive real numbers.

$\sqrt{\frac{32}{4}}$

Answer

$\sqrt{\frac{32}{4}}$

There are two ways to solve this problem. First you can divide the numbers under the radical. Then simplify.

Example 1

$\sqrt{\frac{32}{4}}=\sqrt{8}=\sqrt{4}\cdot\sqrt{2}=2\sqrt{2}$

Example 2

Find the square root of both numerator and denominator, simplifying as much as possible then dividing out like terms.

$\sqrt{\frac{32}{4}}=\frac{\sqrt{32}}{\sqrt{4}}=\frac{\sqrt{16}\cdot \sqrt{2}}{\sqrt{4}}=\frac{4\sqrt{2}}{2}=2\sqrt{2}$

Both methods will give you the correct answer of $2\sqrt{2}$ .

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Question

Simplify:

$\sqrt{\frac{64}{169}}$

Answer

To simplfy, we must first distribute the square root.

$\frac{\sqrt{64}}{\sqrt{169}}$

Next, we can simplify each of the square roots.

$\frac{8}{13}$

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Question

Find the quotient:

$\frac{\sqrt{54}}{\sqrt{45}}$

Answer

Simplify each radical:

$\frac{\sqrt{54}}{\sqrt{45}} = \frac{\sqrt{9\cdot 6}}{\sqrt{9\cdot 5}}=\frac{3\sqrt{6}}{3\sqrt{5}}=\frac{\sqrt{6}}{\sqrt{5}}$

Rationalize the denominator:

$\frac{\sqrt{6}}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}}= \frac{\sqrt{30}}{5}$

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Question

Find the quotient:

$\sqrt{\frac{18}{2}}$

Answer

Find the quotient:

$\frac{\sqrt{18}}{\sqrt{2}}$

There are two ways to approach this problem.

Option 1: Combine the radicals first, the reduce

$\frac{\sqrt{18}}{\sqrt{2}}=\sqrt{\frac{18}{2}}=\sqrt{9}=3$

Option 2: Simplify the radicals first, then reduce

$\frac{\sqrt{18}}{\sqrt{2}}=\frac{\sqrt{9\cdot 2}}{\sqrt{2}}=\frac{3\sqrt{2}}{\sqrt{2}}=3$

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