Solve sqrt{frac{3/2*27}}{27}

$$\frac{ \sqrt{ \frac{ 3 }{ 2 } \times 27 } }{ 27 }$$

Evaluate

$$\frac{\sqrt{2}}{6}\approx 0.23570226$$

Solution Steps

Express \frac{3}{2}\times 27 as a single fraction.

$$\frac{\sqrt{\frac{3\times 27}{2}}}{27}$$

Multiply 3 and 27 to get 81.

$$\frac{\sqrt{\frac{81}{2}}}{27}$$

Rewrite the square root of the division \sqrt{\frac{81}{2}} as the division of square roots \frac{\sqrt{81}}{\sqrt{2}}.

$$\frac{\frac{\sqrt{81}}{\sqrt{2}}}{27}$$

Calculate the square root of 81 and get 9.

$$\frac{\frac{9}{\sqrt{2}}}{27}$$

Rationalize the denominator of \frac{9}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\frac{9\sqrt{2}}{\left(\sqrt{2}\right)^{2}}}{27}$$

The square of \sqrt{2} is 2.

$$\frac{\frac{9\sqrt{2}}{2}}{27}$$

Express \frac{\frac{9\sqrt{2}}{2}}{27} as a single fraction.

$$\frac{9\sqrt{2}}{2\times 27}$$

Cancel out 9 in both numerator and denominator.

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

Multiply 2 and 3 to get 6.

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