Solve sqrt{5}sqrt{10}sqrt{12}=

$$\sqrt { 5 } \sqrt { 10 } \sqrt { 12 } =$$

Evaluate

$$10\sqrt{6}\approx 24.494897428$$

Solution Steps

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

$$\sqrt{5}\sqrt{5}\sqrt{2}\sqrt{12}$$

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

$$5\sqrt{2}\sqrt{12}$$

Factor 12=2\times 6. Rewrite the square root of the product \sqrt{2\times 6} as the product of square roots \sqrt{2}\sqrt{6}.

$$5\sqrt{2}\sqrt{2}\sqrt{6}$$

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

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

Multiply 5 and 2 to get 10.

$$10\sqrt{6}$$