What is $\sqrt{\frac{27}{16}}$ $sqrt(27/16)$ ?

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What is $\sqrt{\frac{27}{16}}$ $sqrt(27/16)$ ?

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Answer 1 · 2015-07-26T22:55:15

I found: $\frac{3}{4} \sqrt{3}$ $3/4sqrt(3)$

Explanation:

You can write your square root as:
$\frac{\sqrt{27}}{\sqrt{16}} = \frac{\sqrt{3 \cdot 9}}{4} = \frac{\sqrt{9} \sqrt{3}}{4} = \frac{3}{4} \sqrt{3}$ $sqrt(27)/sqrt(16)=sqrt(3*9)/4=(sqrt(9)sqrt(3))/4=3/4sqrt(3)$

Answer 2 · 2015-07-26T22:58:03

$\frac{3 \sqrt{3}}{4}$ $(3sqrt(3))/4$

Explanation:

Use the quotient property of radicals to rewrite your expression as

$\sqrt{\frac{27}{16}} = \frac{\sqrt{27}}{\sqrt{16}} = \frac{\sqrt{27}}{4}$ $sqrt(27/16) = sqrt(27)/sqrt(16) = sqrt(27)/4$

Since $27$ $27$ is not a perfect square, you're going to have to see if you can write it as a product of a perfect square and another number

$27 = 9 \cdot 3 = 3^{2} \cdot 3$ $27 = 9 * 3 = 3^2 * 3$

This means that your expression will be

$\frac{\sqrt{3^{2} \cdot 3}}{4} = \frac{\sqrt{3^{2}} \cdot \sqrt{3}}{4} = \frac{3 \sqrt{3}}{4}$ $sqrt(3^2 * 3)/4 = (sqrt(3^2) * sqrt(3))/4 = color(green)((3 sqrt(3))/4)$

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What is $\sqrt{\frac{27}{16}}$ $sqrt(27/16)$ ?

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