# How do you simplify sqrt((32a^4)/b^2)?

May 8, 2017

See the solution process below:

#### Explanation:

We can rewrite this expression as:

$\sqrt{\frac{\left(16 \cdot 2\right) {a}^{4}}{b} ^ 2} \implies \sqrt{\frac{16 {a}^{4}}{b} ^ 2 \cdot 2}$

Using this rule for radicals we can further rewrite this expression as:

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

$\sqrt{\frac{16 {a}^{4}}{b} ^ 2 \cdot 2} \implies \sqrt{\frac{16 {a}^{4}}{b} ^ 2} \cdot \sqrt{2}$

We can now take the square root of the left radical to simplify this expression as:

$\frac{\pm 4 {a}^{2}}{b} \sqrt{2}$

Or, because the original question is given with only the principal root indicated:

$\frac{4 {a}^{2}}{b} \sqrt{2}$