Solve sqrt{81*125/144}

$$\sqrt { \frac { 81 \times 125 } { 144 } }$$

Evaluate

$$\frac{15\sqrt{5}}{4}\approx 8.385254916$$

Solution Steps

Multiply 81 and 125 to get 10125.

$$\sqrt{\frac{10125}{144}}$$

Reduce the fraction \frac{10125}{144} to lowest terms by extracting and canceling out 9.

$$\sqrt{\frac{1125}{16}}$$

Rewrite the square root of the division \sqrt{\frac{1125}{16}} as the division of square roots \frac{\sqrt{1125}}{\sqrt{16}}.

$$\frac{\sqrt{1125}}{\sqrt{16}}$$

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}.

$$\frac{15\sqrt{5}}{\sqrt{16}}$$

Calculate the square root of 16 and get 4.

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