Solve 3sqrt{2}*frac{sqrt{6}}{6}*5sqrt{10}

$$3 \sqrt { 2 } \times \frac { \sqrt { 6 } } { 6 } \times 5 \sqrt { 10 }$$

Evaluate

$$5\sqrt{30}\approx 27.386127875$$

Solution Steps

Factor 10=2\times 5. Rewrite the square root of the product \sqrt{2\times 5} as the product of square roots \sqrt{2}\sqrt{5}.

$$3\times 5\sqrt{2}\times \frac{\sqrt{6}}{6}\sqrt{2}\sqrt{5}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$3\times 5\times 2\times \frac{\sqrt{6}}{6}\sqrt{5}$$

Multiply 3 and 5 to get 15.

$$15\times 2\times \frac{\sqrt{6}}{6}\sqrt{5}$$

Multiply 15 and 2 to get 30.

$$30\times \frac{\sqrt{6}}{6}\sqrt{5}$$

Cancel out 6, the greatest common factor in 30 and 6.

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

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

$$5\sqrt{30}$$