Solve sqrt{75/49}

$$\sqrt { \frac { 75 } { 49 } }$$

Evaluate

$$\frac{5\sqrt{3}}{7}\approx 1.237179148$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{75}{49}} as the division of square roots \frac{\sqrt{75}}{\sqrt{49}}.

$$\frac{\sqrt{75}}{\sqrt{49}}$$

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$\frac{5\sqrt{3}}{\sqrt{49}}$$

Calculate the square root of 49 and get 7.

$$\frac{5\sqrt{3}}{7}$$