Solve sqrt{24/49}

$$\sqrt { \frac { 24 } { 49 } }$$

Evaluate

$$\frac{2\sqrt{6}}{7}\approx 0.699854212$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{24}{49}} as the division of square roots \frac{\sqrt{24}}{\sqrt{49}}.

$$\frac{\sqrt{24}}{\sqrt{49}}$$

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}.

$$\frac{2\sqrt{6}}{\sqrt{49}}$$

Calculate the square root of 49 and get 7.

$$\frac{2\sqrt{6}}{7}$$