Solve 9sqrt{1/27}

$$9 \sqrt { \frac { 1 } { 27 } }$$

Evaluate

$$\sqrt{3}\approx 1.732050808$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{27}} as the division of square roots \frac{\sqrt{1}}{\sqrt{27}}.

$$9\times \frac{\sqrt{1}}{\sqrt{27}}$$

Calculate the square root of 1 and get 1.

$$9\times \frac{1}{\sqrt{27}}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$9\times \frac{1}{3\sqrt{3}}$$

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

$$9\times \frac{\sqrt{3}}{3\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$9\times \frac{\sqrt{3}}{3\times 3}$$

Multiply 3 and 3 to get 9.

$$9\times \frac{\sqrt{3}}{9}$$

Cancel out 9 and 9.

$$\sqrt{3}$$