How do you simplify sqrt(27/16)?

Jul 12, 2017

It is $\frac{3 \times \sqrt{3}}{4}$

Explanation:

$\frac{\sqrt{27}}{4}$

since $\sqrt{16} = 4$

You can further write

$\frac{\sqrt{9 \times 3}}{4} = \frac{3 \times \left(\sqrt{3}\right)}{4}$

$\frac{3 \times \left(\sqrt{3}\right)}{4}$

Jul 12, 2017

$\frac{3 \sqrt{3}}{4}$

Explanation:

Value $= \sqrt{\frac{27}{16}}$

Expressing the numerator and denominator as their prime factors:

Value $= \sqrt{\frac{3 \times 3 \times 3}{2 \times 2 \times 2 \times 2}}$

Taking each pair of factors once through the sqrt.

Value $= \frac{3 \sqrt{3}}{2 \times 2}$

$= \frac{3 \sqrt{3}}{4}$