Solve frac{sqrt{(2^-1)}}{3^2}

$$\frac { \sqrt { ( 2 ^ { - 1 } ) } } { 3 ^ { 2 } }$$

Evaluate

$$\frac{\sqrt{2}}{18}\approx 0.07856742$$

Solution Steps

Calculate 2 to the power of -1 and get \frac{1}{2}.

$$\frac{\sqrt{\frac{1}{2}}}{3^{2}}$$

Rewrite the square root of the division \sqrt{\frac{1}{2}} as the division of square roots \frac{\sqrt{1}}{\sqrt{2}}.

$$\frac{\frac{\sqrt{1}}{\sqrt{2}}}{3^{2}}$$

Calculate the square root of 1 and get 1.

$$\frac{\frac{1}{\sqrt{2}}}{3^{2}}$$

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

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

Calculate 3 to the power of 2 and get 9.

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

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

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

Multiply 2 and 9 to get 18.

$$\frac{\sqrt{2}}{18}$$