Evaluate fifth root of 7 19/32

$\sqrt[5]{7 \frac{19}{32}}$

Convert $7 \frac{19}{32}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$\sqrt[5]{7 + \frac{19}{32}}$

Add $7$ and $\frac{19}{32}$ .

To write $7$ as a fraction with a common denominator, multiply by $\frac{32}{32}$ .

$\sqrt[5]{7 \cdot \frac{32}{32} + \frac{19}{32}}$

Combine $7$ and $\frac{32}{32}$ .

$\sqrt[5]{\frac{7 \cdot 32}{32} + \frac{19}{32}}$

Combine the numerators over the common denominator.

$\sqrt[5]{\frac{7 \cdot 32 + 19}{32}}$

Simplify the numerator.

Multiply $7$ by $32$ .

$\sqrt[5]{\frac{224 + 19}{32}}$

Add $224$ and $19$ .

$\sqrt[5]{\frac{243}{32}}$

Rewrite $\sqrt[5]{\frac{243}{32}}$ as $\frac{\sqrt[5]{243}}{\sqrt[5]{32}}$ .

$\frac{\sqrt[5]{243}}{\sqrt[5]{32}}$

Simplify the numerator.

Rewrite $243$ as $3^{5}$ .

$\frac{\sqrt[5]{3^{5}}}{\sqrt[5]{32}}$

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

$\frac{3}{\sqrt[5]{32}}$

Simplify the denominator.

Rewrite $32$ as $2^{5}$ .

$\frac{3}{\sqrt[5]{2^{5}}}$

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

$\frac{3}{2}$

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{2}$

Decimal Form:

$1.5$

Mixed Number Form:

$1 \frac{1}{2}$