Solve 9/sqrt[4]{36}

$$\frac { 9 } { \sqrt[ 4 ] { 36 } }$$

Evaluate

$$\frac{3\sqrt{6}}{2}\approx 3.674234614$$

Solution Steps

Rewrite \sqrt[4]{36} as \sqrt[4]{6^{2}}. Convert from radical to exponential form and cancel out 2 in the exponent. Convert back to radical form.

$$\sqrt[4]{36}=\sqrt[4]{6^{2}}=6^{\frac{2}{4}}=6^{\frac{1}{2}}=\sqrt{6}$$

Insert the obtained value back in the expression.

$$\frac{9}{\sqrt{6}}$$

Rationalize the denominator of \frac{9}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{9\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{9\sqrt{6}}{6}$$

Divide 9\sqrt{6} by 6 to get \frac{3}{2}\sqrt{6}.

$$\frac{3}{2}\sqrt{6}$$