Solve sqrt{48/10}

$$\sqrt { 4 \frac { 8 } { 10 } }$$

Evaluate

$$\frac{2\sqrt{30}}{5}\approx 2.19089023$$

Solution Steps

Multiply 4 and 10 to get 40.

$$\sqrt{\frac{40+8}{10}}$$

Add 40 and 8 to get 48.

$$\sqrt{\frac{48}{10}}$$

Reduce the fraction \frac{48}{10} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{24}{5}}$$

Rewrite the square root of the division \sqrt{\frac{24}{5}} as the division of square roots \frac{\sqrt{24}}{\sqrt{5}}.

$$\frac{\sqrt{24}}{\sqrt{5}}$$

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$\frac{2\sqrt{6}}{\sqrt{5}}$$

Rationalize the denominator of \frac{2\sqrt{6}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{2\sqrt{6}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{2\sqrt{6}\sqrt{5}}{5}$$

To multiply \sqrt{6} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{2\sqrt{30}}{5}$$