Solve frac{sqrt[10]{32}}{8sqrt{4}}

$$\frac { \sqrt[ 10 ] { 32 } } { 8 \sqrt { 4 } }$$

Evaluate

$$\frac{\sqrt{2}}{16}\approx 0.088388348$$

Solution Steps

Rewrite \sqrt[10]{32} as \sqrt[10]{2^{5}}. Convert from radical to exponential form and cancel out 5 in the exponent. Convert back to radical form.

$$\sqrt[10]{32}=\sqrt[10]{2^{5}}=2^{\frac{5}{10}}=2^{\frac{1}{2}}=\sqrt{2}$$

Insert the obtained value back in the expression.

$$\frac{\sqrt{2}}{8\sqrt{4}}$$

Calculate the square root of 4 and get 2.

$$\frac{\sqrt{2}}{8\times 2}$$

Multiply 8 and 2 to get 16.

$$\frac{\sqrt{2}}{16}$$