Solve sqrt{75/7}

$$\sqrt { \frac { 75 } { 7 } }$$

Evaluate

$$\frac{5\sqrt{21}}{7}\approx 3.273268354$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{75}{7}} as the division of square roots \frac{\sqrt{75}}{\sqrt{7}}.

$$\frac{\sqrt{75}}{\sqrt{7}}$$

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}.

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

Rationalize the denominator of \frac{5\sqrt{3}}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{5\sqrt{3}\sqrt{7}}{\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

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

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

$$\frac{5\sqrt{21}}{7}$$