Solve 1/2sqrt[4]{4}

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

Evaluate

$$\frac{\sqrt{2}}{4}\approx 0.353553391$$

Solution Steps

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.

$$\frac{1}{2\sqrt{2}}$$

Rationalize the denominator of \frac{1}{2\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

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

Multiply 2 and 2 to get 4.

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