Solve 3/5sqrt{30}*6/5sqrt{5}

$$\frac { 3 } { 5 } \sqrt { 30 } \cdot \frac { 6 } { 5 } \sqrt { 5 }$$

Evaluate

$$\frac{18\sqrt{6}}{5}\approx 8.818163074$$

Solution Steps

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}.

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

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

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

Cancel out 5 and 5.

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

Express 3\times \frac{6}{5} as a single fraction.

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

Multiply 3 and 6 to get 18.

$$\frac{18}{5}\sqrt{6}$$