How do you simplify $\sqrt{\frac{27}{64}}$ $sqrt (27 / 64)$ ?

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Answer 1 · 2016-02-08T18:42:45

$\frac{3 \sqrt{3}}{8}$ $(3sqrt3)/8$

We can begin be re writing the square root as:

$\sqrt{\frac{27}{64}} = \frac{\sqrt{27}}{\sqrt{64}}$ $sqrt(27/64) = sqrt(27)/sqrt(64)$

Luckily, 64 is a square number so that will allow us to get rid of the square root on the bottom:

$= \frac{\sqrt{27}}{8}$ $=sqrt(27)/8$

Now we can transform $\sqrt{27}$ $sqrt(27)$ into a surd like so:

$\sqrt{27} = \sqrt{9 \cdot 3} = \sqrt{9} \cdot \sqrt{3} = 3 \sqrt{3}$ $sqrt(27) = sqrt(9*3) = sqrt(9)*sqrt(3) = 3sqrt3$

So the fraction can be re written as:

$\frac{3 \sqrt{3}}{8}$ $(3sqrt3)/8$

How do you simplify sqrt (27 / 64)√2764sqrt (27 / 64)?