Solve sqrt{112/3}

$$\sqrt { \frac { 112 } { 3 } }$$

Evaluate

$$\frac{4\sqrt{21}}{3}\approx 6.110100927$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{112}{3}} as the division of square roots \frac{\sqrt{112}}{\sqrt{3}}.

$$\frac{\sqrt{112}}{\sqrt{3}}$$

Factor 112=4^{2}\times 7. Rewrite the square root of the product \sqrt{4^{2}\times 7} as the product of square roots \sqrt{4^{2}}\sqrt{7}. Take the square root of 4^{2}.

$$\frac{4\sqrt{7}}{\sqrt{3}}$$

Rationalize the denominator of \frac{4\sqrt{7}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{4\sqrt{7}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{4\sqrt{7}\sqrt{3}}{3}$$

To multiply \sqrt{7} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{4\sqrt{21}}{3}$$