Solve (-27)^frac{1{3}}(1/6sqrt{2}-1/4sqrt{32})

$$( - 27 ) ^ { \frac { 1 } { 3 } } ( \frac { 1 } { 6 } \sqrt { 2 } - \frac { 1 } { 4 } \sqrt { 32 } )$$

Evaluate

$$\frac{5\sqrt{2}}{2}\approx 3.535533906$$

Solution Steps

Calculate -27 to the power of \frac{1}{3} and get -3.

$$-3\left(\frac{1}{6}\sqrt{2}-\frac{1}{4}\sqrt{32}\right)$$

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}.

$$-3\left(\frac{1}{6}\sqrt{2}-\frac{1}{4}\times 4\sqrt{2}\right)$$

Multiply -\frac{1}{4} and 4 to get -1.

$$-3\left(\frac{1}{6}\sqrt{2}-\sqrt{2}\right)$$

Combine \frac{1}{6}\sqrt{2} and -\sqrt{2} to get -\frac{5}{6}\sqrt{2}.

$$-3\left(-\frac{5}{6}\right)\sqrt{2}$$

Multiply -3 and -\frac{5}{6} to get \frac{5}{2}.

$$\frac{5}{2}\sqrt{2}$$