Solve sqrt{48/1125}

$$\sqrt { \frac { 48 } { 1125 } }$$

Evaluate

$$\frac{4\sqrt{15}}{75}\approx 0.206559112$$

Solution Steps

Reduce the fraction \frac{48}{1125} to lowest terms by extracting and canceling out 3.

$$\sqrt{\frac{16}{375}}$$

Rewrite the square root of the division \sqrt{\frac{16}{375}} as the division of square roots \frac{\sqrt{16}}{\sqrt{375}}.

$$\frac{\sqrt{16}}{\sqrt{375}}$$

Calculate the square root of 16 and get 4.

$$\frac{4}{\sqrt{375}}$$

Factor 375=5^{2}\times 15. Rewrite the square root of the product \sqrt{5^{2}\times 15} as the product of square roots \sqrt{5^{2}}\sqrt{15}. Take the square root of 5^{2}.

$$\frac{4}{5\sqrt{15}}$$

Rationalize the denominator of \frac{4}{5\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.

$$\frac{4\sqrt{15}}{5\left(\sqrt{15}\right)^{2}}$$

The square of \sqrt{15} is 15.

$$\frac{4\sqrt{15}}{5\times 15}$$

Multiply 5 and 15 to get 75.

$$\frac{4\sqrt{15}}{75}$$