# How do you simplify sqrt(28a^2b^3)?

Oct 17, 2016

#### Answer:

$2 \sqrt{7} a {b}^{\frac{3}{2}}$

#### Explanation:

The easiest way to simplify this surd is to separate it into its constituent surds, that is, the surds that make it up:

$\sqrt{a b} = \sqrt{a} \times \sqrt{b}$

So if we apply the same rule to $\sqrt{28 {a}^{2} {b}^{3}}$ we get:

sqrt(28a^2b^3) = sqrt28xxsqrt(a^2)xxsqrt(b^3

We can do this again with each of these surds to simplify it again:

$\sqrt{28} \times \sqrt{{a}^{2}} \times \sqrt{{b}^{3}} = \sqrt{4} \times \sqrt{7} \times \sqrt{a} \times \sqrt{a} \times \sqrt{b} \times \sqrt{b} \times \sqrt{b}$

We can evaluate these surds by separating them into like factors:

$\sqrt{4} \times \sqrt{7} = 2 \times \sqrt{7} = 2 \sqrt{7}$
$\sqrt{a} \times \sqrt{a} = a$
$\sqrt{b} \times \sqrt{b} \times \sqrt{b} = b \sqrt{b} = {b}^{\frac{3}{2}}$

Now we need to multiply each of these factors:

$2 \sqrt{7} a {b}^{\frac{3}{2}}$