Solve =sqrt{48/5}

$$= \sqrt { \frac { 48 } { 5 } }$$

Evaluate

$$\frac{4\sqrt{15}}{5}\approx 3.098386677$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{48}{5}} as the division of square roots \frac{\sqrt{48}}{\sqrt{5}}.

$$\frac{\sqrt{48}}{\sqrt{5}}$$

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$\frac{4\sqrt{3}}{\sqrt{5}}$$

Rationalize the denominator of \frac{4\sqrt{3}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{4\sqrt{3}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{4\sqrt{3}\sqrt{5}}{5}$$

To multiply \sqrt{3} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{4\sqrt{15}}{5}$$