Solve frac{sqrt[6]{27}}{sqrt{3}}

$$\frac{ \sqrt[ 6 ]{ 27 } }{ \sqrt{ 3 } }$$

Evaluate

$$1$$

Solution Steps

Rewrite \sqrt[6]{27} as \sqrt[6]{3^{3}}. Convert from radical to exponential form and cancel out 3 in the exponent. Convert back to radical form.

$$\sqrt[6]{27}=\sqrt[6]{3^{3}}=3^{\frac{3}{6}}=3^{\frac{1}{2}}=\sqrt{3}$$

Insert the obtained value back in the expression.

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

Rewrite the division of square roots \frac{\sqrt{3}}{\sqrt{3}} as the square root of the division \sqrt{\frac{3}{3}} and perform the division.

$$\sqrt{1}$$

Calculate the square root of 1 and get 1.

$$1$$

Factor

$$1$$