Solve sqrt{48/162}=

$$\sqrt { \frac { 48 } { 162 } } =$$

Evaluate

$$\frac{2\sqrt{6}}{9}\approx 0.544331054$$

Solution Steps

Reduce the fraction \frac{48}{162} to lowest terms by extracting and canceling out 6.

$$\sqrt{\frac{8}{27}}$$

Rewrite the square root of the division \sqrt{\frac{8}{27}} as the division of square roots \frac{\sqrt{8}}{\sqrt{27}}.

$$\frac{\sqrt{8}}{\sqrt{27}}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

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

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}.

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

Rationalize the denominator of \frac{2\sqrt{2}}{3\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{2\sqrt{6}}{3\times 3}$$

Multiply 3 and 3 to get 9.

$$\frac{2\sqrt{6}}{9}$$