Solve frac{{sqrt{32}}-0}{6}5sqrt[3]{-216}

$$\frac { { \sqrt { 32 } } - 0 } { 6 }5 \sqrt[ 3 ] { - 216 }$$

Evaluate

$$-20\sqrt{2}\approx -28.284271247$$

Solution Steps

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$5\times \frac{4\sqrt{2}-0}{6}\sqrt[3]{-216}$$

Calculate \sqrt[3]{-216} and get -6.

$$5\times \frac{4\sqrt{2}-0}{6}\left(-6\right)$$

Multiply 5 and -6 to get -30.

$$-30\times \frac{4\sqrt{2}-0}{6}$$

Cancel out 6, the greatest common factor in 30 and 6.

$$-5\left(4\sqrt{2}-0\right)$$

Multiply -1 and 0 to get 0.

$$-5\times 4\sqrt{2}$$

Multiply -5 and 4 to get -20.

$$-20\sqrt{2}$$