Solve sqrt{120}*sqrt{27}*sqrt{5}

$$\sqrt { 120 } \times \sqrt { 27 } \times \sqrt { 5 }$$

Evaluate

$$90\sqrt{2}\approx 127.279220614$$

Solution Steps

Factor 120=5\times 24. Rewrite the square root of the product \sqrt{5\times 24} as the product of square roots \sqrt{5}\sqrt{24}.

$$\sqrt{5}\sqrt{24}\sqrt{27}\sqrt{5}$$

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

$$5\sqrt{27}\sqrt{24}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$5\times 3\sqrt{3}\sqrt{24}$$

Multiply 5 and 3 to get 15.

$$15\sqrt{3}\sqrt{24}$$

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}.

$$15\sqrt{3}\times 2\sqrt{6}$$

Multiply 15 and 2 to get 30.

$$30\sqrt{3}\sqrt{6}$$

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}.

$$30\sqrt{3}\sqrt{3}\sqrt{2}$$

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

$$30\times 3\sqrt{2}$$

Multiply 30 and 3 to get 90.

$$90\sqrt{2}$$