Evaluate fourth root of 625/256

$\sqrt[4]{\frac{625}{256}}$

Step 1

Rewrite $\sqrt[4]{\frac{625}{256}}$ as $\frac{\sqrt[4]{625}}{\sqrt[4]{256}}$ .

$\frac{\sqrt[4]{625}}{\sqrt[4]{256}}$

Step 2

Simplify the numerator.

Rewrite $625$ as $5^{4}$ .

$\frac{\sqrt[4]{5^{4}}}{\sqrt[4]{256}}$

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

$\frac{5}{\sqrt[4]{256}}$

Step 3

Simplify the denominator.

Rewrite $256$ as $4^{4}$ .

$\frac{5}{\sqrt[4]{4^{4}}}$

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

$\frac{5}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{4}$

Decimal Form:

$1.25$

Mixed Number Form:

$1 \frac{1}{4}$