Solve sqrt{45}*sqrt{5/9}*sqrt{6}

$$\sqrt { 45 } \times \sqrt { \frac { 5 } { 9 } } \times \sqrt { 6 }$$

Evaluate

$$5\sqrt{6}\approx 12.247448714$$

Solution Steps

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

$$3\sqrt{5}\sqrt{\frac{5}{9}}\sqrt{6}$$

Rewrite the square root of the division \sqrt{\frac{5}{9}} as the division of square roots \frac{\sqrt{5}}{\sqrt{9}}.

$$3\sqrt{5}\times \frac{\sqrt{5}}{\sqrt{9}}\sqrt{6}$$

Calculate the square root of 9 and get 3.

$$3\sqrt{5}\times \frac{\sqrt{5}}{3}\sqrt{6}$$

Cancel out 3 and 3.

$$\sqrt{5}\sqrt{5}\sqrt{6}$$

To multiply \sqrt{5} and \sqrt{6}, multiply the numbers under the square root.

$$\sqrt{30}\sqrt{5}$$

Factor 30=5\times 6. Rewrite the square root of the product \sqrt{5\times 6} as the product of square roots \sqrt{5}\sqrt{6}.

$$\sqrt{5}\sqrt{6}\sqrt{5}$$

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

$$5\sqrt{6}$$