Solve sqrt{frac{3/9}}{sqrt[1/3]{90}}

$$\frac { \sqrt { \frac { 3 } { 9 } } } { \sqrt[ \frac { 1 } { 3 } ] { 90 } }$$

Evaluate

$$\frac{\sqrt{3}}{2187000}\approx 0.000000792$$

Solution Steps

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$\frac{\sqrt{\frac{1}{3}}}{\sqrt[\frac{1}{3}]{90}}$$

Rewrite the square root of the division \sqrt{\frac{1}{3}} as the division of square roots \frac{\sqrt{1}}{\sqrt{3}}.

$$\frac{\frac{\sqrt{1}}{\sqrt{3}}}{\sqrt[\frac{1}{3}]{90}}$$

Calculate the square root of 1 and get 1.

$$\frac{\frac{1}{\sqrt{3}}}{\sqrt[\frac{1}{3}]{90}}$$

Rationalize the denominator of \frac{1}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}{\sqrt[\frac{1}{3}]{90}}$$

The square of \sqrt{3} is 3.

$$\frac{\frac{\sqrt{3}}{3}}{\sqrt[\frac{1}{3}]{90}}$$

Calculate \sqrt[\frac{1}{3}]{90} and get 729000.

$$\frac{\frac{\sqrt{3}}{3}}{729000}$$

Express \frac{\frac{\sqrt{3}}{3}}{729000} as a single fraction.

$$\frac{\sqrt{3}}{3\times 729000}$$

Multiply 3 and 729000 to get 2187000.

$$\frac{\sqrt{3}}{2187000}$$