Simplify 1/8 fourth root of 7+3/8 fourth root of 7

$\frac{1}{8} \sqrt[4]{7} + \frac{3}{8} \sqrt[4]{7}$

Step 1

Simplify each term.

Combine $\frac{1}{8}$ and $\sqrt[4]{7}$ .

$\frac{\sqrt[4]{7}}{8} + \frac{3}{8} \cdot \sqrt[4]{7}$

Combine $\frac{3}{8}$ and $\sqrt[4]{7}$ .

$\frac{\sqrt[4]{7}}{8} + \frac{3 \sqrt[4]{7}}{8}$

Step 2

Simplify terms.

Combine the numerators over the common denominator.

$\frac{\sqrt[4]{7} + 3 \sqrt[4]{7}}{8}$

Add $\sqrt[4]{7}$ and $3 \sqrt[4]{7}$ .

$\frac{4 \sqrt[4]{7}}{8}$

Cancel the common factor of $4$ and $8$ .

Factor $4$ out of $4 \sqrt[4]{7}$ .

$\frac{4 (\sqrt[4]{7})}{8}$

Cancel the common factors.

Factor $4$ out of $8$ .

$\frac{4 \sqrt[4]{7}}{4 \cdot 2}$

Cancel the common factor.

$\frac{4 \sqrt[4]{7}}{4 \cdot 2}$

Rewrite the expression.

$\frac{\sqrt[4]{7}}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt[4]{7}}{2}$

Decimal Form:

$0.81328828 \dots$