Simplify (3 square root of 32a^2)/( square root of 8a)

$\frac{3 \sqrt{32 a^{2}}}{\sqrt{8 a}}$

Combine $\sqrt{32 a^{2}}$ and $\sqrt{8 a}$ into a single radical.

$3 \sqrt{\frac{32 a^{2}}{8 a}}$

Reduce the expression $\frac{32 a^{2}}{8 a}$ by cancelling the common factors.

Factor $8$ out of $32 a^{2}$ .

$3 \sqrt{\frac{8 (4 a^{2})}{8 a}}$

Factor $8$ out of $8 a$ .

$3 \sqrt{\frac{8 (4 a^{2})}{8 (a)}}$

Cancel the common factor.

$3 \sqrt{\frac{8 (4 a^{2})}{8 a}}$

Rewrite the expression.

$3 \sqrt{\frac{4 a^{2}}{a}}$

Cancel the common factor of $a^{2}$ and $a$ .

Factor $a$ out of $4 a^{2}$ .

$3 \sqrt{\frac{a (4 a)}{a}}$

Cancel the common factors.

Raise $a$ to the power of $1$ .

$3 \sqrt{\frac{a (4 a)}{a^{1}}}$

Factor $a$ out of $a^{1}$ .

$3 \sqrt{\frac{a (4 a)}{a \cdot 1}}$

Cancel the common factor.

$3 \sqrt{\frac{a (4 a)}{a \cdot 1}}$

Rewrite the expression.

$3 \sqrt{\frac{4 a}{1}}$

Divide $4 a$ by $1$ .

$3 \sqrt{4 a}$

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

$3 \sqrt{2^{2} a}$

Pull terms out from under the radical.

$3 (2 \sqrt{a})$

Multiply $2$ by $3$ .

$6 \sqrt{a}$