Solve sqrt{15}sqrt{20}sqrt{24}=

$$\sqrt { 15 } \sqrt { 20 } \sqrt { 24 } =$$

Evaluate

$$60\sqrt{2}\approx 84.852813742$$

Solution Steps

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$\sqrt{15}\times 2\sqrt{5}\sqrt{24}$$

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

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

Multiply 2 and 2 to get 4.

$$\sqrt{15}\times 4\sqrt{5}\sqrt{6}$$

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}.

$$\sqrt{5}\sqrt{3}\times 4\sqrt{5}\sqrt{6}$$

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

$$5\times 4\sqrt{3}\sqrt{6}$$

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}.

$$5\times 4\sqrt{3}\sqrt{3}\sqrt{2}$$

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

$$5\times 4\times 3\sqrt{2}$$

Multiply 5 and 4 to get 20.

$$20\times 3\sqrt{2}$$

Multiply 20 and 3 to get 60.

$$60\sqrt{2}$$