Solve frac{6sqrt{1125}}{sqrt{20}}

$$\frac { 6 \sqrt { 1125 } } { \sqrt { 20 } }$$

Evaluate

$$45$$

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}.

$$\frac{6\times 15\sqrt{5}}{\sqrt{20}}$$

Multiply 6 and 15 to get 90.

$$\frac{90\sqrt{5}}{\sqrt{20}}$$

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$\frac{90\sqrt{5}}{2\sqrt{5}}$$

Cancel out 2\sqrt{5} in both numerator and denominator.

$$45$$

Factor

$$3^{2}\times 5$$