# How do you simplify 4 sqrt (81/16)?

Aug 7, 2016

$\frac{3}{2}$

#### Explanation:

If you recognise 81 and 16 as being 4th powers, the answer is easy to write down as $\frac{3}{2}$

Otherwise write each number as the product of its prime factors:

$\sqrt[4]{\frac{81}{16}} = \sqrt[4]{\frac{3 \times 3 \times 3 \times 3}{2 \times 2 \times 2 \times 2}} = \sqrt[4]{\frac{{3}^{4}}{{2}^{4}}} = \frac{3}{2}$

The 4th root is easy to find if you remember it is the square root of a square root.

81 and 16 are both perfect squares, but their square roots are also squares.

$\sqrt[4]{\frac{81}{16}} = \sqrt{\sqrt{\frac{81}{16}}} = \sqrt{\frac{9}{4}} = \frac{3}{2}$