Solve 4/sqrt[4]{9}

$$\frac { 4 } { \sqrt[ 4 ] { 9 } }$$

Evaluate

$$\frac{4\sqrt{3}}{3}\approx 2.309401077$$

Solution Steps

Rewrite \sqrt[4]{9} as \sqrt[4]{3^{2}}. Convert from radical to exponential form and cancel out 2 in the exponent. Convert back to radical form.

$$\sqrt[4]{9}=\sqrt[4]{3^{2}}=3^{\frac{2}{4}}=3^{\frac{1}{2}}=\sqrt{3}$$

Insert the obtained value back in the expression.

$$\frac{4}{\sqrt{3}}$$

Rationalize the denominator of \frac{4}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{4\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{4\sqrt{3}}{3}$$