Solve sqrt[3]{8}divsqrt[4]{4}

$$\sqrt[ 3 ] { 8 } \div \sqrt[ 4 ] { 4 }$$

Evaluate

$$\sqrt{2}\approx 1.414213562$$

Solution Steps

Calculate \sqrt[3]{8} and get 2.

$$\frac{2}{\sqrt[4]{4}}$$

Rewrite \sqrt[4]{4} as \sqrt[4]{2^{2}}. Convert from radical to exponential form and cancel out 2 in the exponent. Convert back to radical form.

$$\sqrt[4]{4}=\sqrt[4]{2^{2}}=2^{\frac{2}{4}}=2^{\frac{1}{2}}=\sqrt{2}$$

Insert the obtained value back in the expression.

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

Rationalize the denominator of \frac{2}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{2\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

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

Cancel out 2 and 2.

$$\sqrt{2}$$