Simplify ( square root of 72)/( fourth root of 64)

$\frac{\sqrt{72}}{\sqrt[4]{64}}$

Simplify the numerator.

Rewrite $72$ as $6^{2} \cdot 2$ .

Factor $36$ out of $72$ .

$\frac{\sqrt{36 (2)}}{\sqrt[4]{64}}$

Rewrite $36$ as $6^{2}$ .

$\frac{\sqrt{6^{2} \cdot 2}}{\sqrt[4]{64}}$

Pull terms out from under the radical.

$\frac{6 \sqrt{2}}{\sqrt[4]{64}}$

Simplify the denominator.

Rewrite $64$ as $2^{4} \cdot 4$ .

Factor $16$ out of $64$ .

$\frac{6 \sqrt{2}}{\sqrt[4]{16 (4)}}$

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

$\frac{6 \sqrt{2}}{\sqrt[4]{2^{4} \cdot 4}}$

Pull terms out from under the radical.

$\frac{6 \sqrt{2}}{2 \sqrt[4]{4}}$

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

$\frac{6 \sqrt{2}}{2 \sqrt[4]{2^{2}}}$

Rewrite $\sqrt[4]{2^{2}}$ as $\sqrt{\sqrt{2^{2}}}$ .

$\frac{6 \sqrt{2}}{2 \sqrt{\sqrt{2^{2}}}}$

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

$\frac{6 \sqrt{2}}{2 \sqrt{2}}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $6$ and $2$ .

Factor $2$ out of $6 \sqrt{2}$ .

$\frac{2 (3 \sqrt{2})}{2 \sqrt{2}}$

Cancel the common factors.

Factor $2$ out of $2 \sqrt{2}$ .

$\frac{2 (3 \sqrt{2})}{2 (\sqrt{2})}$

Cancel the common factor.

$\frac{2 (3 \sqrt{2})}{2 \sqrt{2}}$

Rewrite the expression.

$\frac{3 \sqrt{2}}{\sqrt{2}}$

Cancel the common factor of $\sqrt{2}$ .

Cancel the common factor.

$\frac{3 \sqrt{2}}{\sqrt{2}}$

Divide $3$ by $1$ .

$3$