Simplify ( square root of 32a)/( square root of 2a)

$\frac{\sqrt{32 a}}{\sqrt{2 a}}$

Combine $\sqrt{32 a}$ and $\sqrt{2 a}$ into a single radical.

$\sqrt{\frac{32 a}{2 a}}$

Reduce the expression $\frac{32 a}{2 a}$ by cancelling the common factors.

Factor $2$ out of $32 a$ .

$\sqrt{\frac{2 (16 a)}{2 a}}$

Factor $2$ out of $2 a$ .

$\sqrt{\frac{2 (16 a)}{2 (a)}}$

Cancel the common factor.

$\sqrt{\frac{2 (16 a)}{2 a}}$

Rewrite the expression.

$\sqrt{\frac{16 a}{a}}$

Cancel the common factor of $a$ .

Cancel the common factor.

$\sqrt{\frac{16 a}{a}}$

Divide $16$ by $1$ .

$\sqrt{16}$

Simplify the expression.

Rewrite $16$ as $4^{2}$ .

$\sqrt{4^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$4$