Evaluate cube root of 343+3/4 cube root of -8

$\sqrt[3]{343} + \frac{3}{4} \sqrt[3]{- 8}$

Simplify each term.

Rewrite $343$ as $7^{3}$ .

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

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

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

Rewrite $- 8$ as ${(- 2)}^{3}$ .

$7 + \frac{3}{4} \cdot \sqrt[3]{{(- 2)}^{3}}$

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

$7 + \frac{3}{4} \cdot - 2$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$7 + \frac{3}{2 (2)} \cdot - 2$

Factor $2$ out of $- 2$ .

$7 + \frac{3}{2 \cdot 2} \cdot (2 \cdot - 1)$

Cancel the common factor.

$7 + \frac{3}{2 \cdot 2} \cdot (2 \cdot - 1)$

Rewrite the expression.

$7 + \frac{3}{2} \cdot - 1$

Combine $\frac{3}{2}$ and $- 1$ .

$7 + \frac{3 \cdot - 1}{2}$

Multiply $3$ by $- 1$ .

$7 + \frac{- 3}{2}$

Move the negative in front of the fraction.

$7 - \frac{3}{2}$

To write $7$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$7 \cdot \frac{2}{2} - \frac{3}{2}$

Combine $7$ and $\frac{2}{2}$ .

$\frac{7 \cdot 2}{2} - \frac{3}{2}$

Combine the numerators over the common denominator.

$\frac{7 \cdot 2 - 3}{2}$

Simplify the numerator.

Multiply $7$ by $2$ .

$\frac{14 - 3}{2}$

Subtract $3$ from $14$ .

$\frac{11}{2}$

The result can be shown in multiple forms.

Exact Form:

$\frac{11}{2}$

Decimal Form:

$5.5$

Mixed Number Form:

$5 \frac{1}{2}$