Solve sqrt{5}sqrt{6}sqrt{15}=

$$\sqrt { 5 } \sqrt { 6 } \sqrt { 15 } =$$

Evaluate

$$15\sqrt{2}\approx 21.213203436$$

Solution Steps

Factor 15=5\times 3. Rewrite the square root of the product \sqrt{5\times 3} as the product of square roots \sqrt{5}\sqrt{3}.

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

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

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

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

$$5\sqrt{3}\sqrt{2}\sqrt{3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

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

Multiply 5 and 3 to get 15.

$$15\sqrt{2}$$