Solve frac{8sqrt{1125}}{sqrt{15}}

$$\frac { 8 \sqrt { 1125 } } { \sqrt { 15 } }$$

Evaluate

$$40\sqrt{3}\approx 69.282032303$$

Solution Steps

Factor 1125=15^{2}\times 5. Rewrite the square root of the product \sqrt{15^{2}\times 5} as the product of square roots \sqrt{15^{2}}\sqrt{5}. Take the square root of 15^{2}.

$$\frac{8\times 15\sqrt{5}}{\sqrt{15}}$$

Multiply 8 and 15 to get 120.

$$\frac{120\sqrt{5}}{\sqrt{15}}$$

Rationalize the denominator of \frac{120\sqrt{5}}{\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.

$$\frac{120\sqrt{5}\sqrt{15}}{\left(\sqrt{15}\right)^{2}}$$

The square of \sqrt{15} is 15.

$$\frac{120\sqrt{5}\sqrt{15}}{15}$$

Factor 15=5\times 3. Rewrite the square root of the product \sqrt{5\times 3} as the product of square roots \sqrt{5}\sqrt{3}.

$$\frac{120\sqrt{5}\sqrt{5}\sqrt{3}}{15}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$\frac{120\times 5\sqrt{3}}{15}$$

Multiply 120 and 5 to get 600.

$$\frac{600\sqrt{3}}{15}$$

Divide 600\sqrt{3} by 15 to get 40\sqrt{3}.

$$40\sqrt{3}$$