Solve frac{+sqrt{32}}{8}-sqrt[4]{-64}=

$$\frac { + \sqrt { 32 } } { 8 } - \sqrt[ 4 ] { - 64 } =$$

Evaluate (complex solution)

$$\frac{\sqrt{2}}{2}+\left(-2-2i\right)\approx -1.292893219-2i$$

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}.

$$\frac{4\sqrt{2}}{8}-\sqrt[4]{-64}$$

Divide 4\sqrt{2} by 8 to get \frac{1}{2}\sqrt{2}.

$$\frac{1}{2}\sqrt{2}-\sqrt[4]{-64}$$

Evaluate

$$\text{Indeterminate}$$

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}.

$$\frac{4\sqrt{2}}{8}-\sqrt[4]{-64}$$

Divide 4\sqrt{2} by 8 to get \frac{1}{2}\sqrt{2}.

$$\frac{1}{2}\sqrt{2}-\sqrt[4]{-64}$$

Factor (complex solution)

$$\frac{\sqrt{2}}{2}+\left(-2-2i\right)$$