Solve sqrt{28/75}

$$\sqrt { \frac { 28 } { 75 } }$$

Evaluate

$$\frac{2\sqrt{21}}{15}\approx 0.611010093$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{28}{75}} as the division of square roots \frac{\sqrt{28}}{\sqrt{75}}.

$$\frac{\sqrt{28}}{\sqrt{75}}$$

Factor 28=2^{2}\times 7. Rewrite the square root of the product \sqrt{2^{2}\times 7} as the product of square roots \sqrt{2^{2}}\sqrt{7}. Take the square root of 2^{2}.

$$\frac{2\sqrt{7}}{\sqrt{75}}$$

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}.

$$\frac{2\sqrt{7}}{5\sqrt{3}}$$

Rationalize the denominator of \frac{2\sqrt{7}}{5\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

$$\frac{2\sqrt{7}\sqrt{3}}{5\times 3}$$

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

$$\frac{2\sqrt{21}}{5\times 3}$$

Multiply 5 and 3 to get 15.

$$\frac{2\sqrt{21}}{15}$$