Solve (sqrt{120})*(4sqrt{6})

$$( \sqrt { 120 } ) \times ( 4 \sqrt { 6 } )$$

Evaluate

$$48\sqrt{5}\approx 107.33126292$$

Solution Steps

Factor 120=6\times 20. Rewrite the square root of the product \sqrt{6\times 20} as the product of square roots \sqrt{6}\sqrt{20}.

$$\sqrt{6}\sqrt{20}\times 4\sqrt{6}$$

Multiply \sqrt{6} and \sqrt{6} to get 6.

$$6\times 4\sqrt{20}$$

Multiply 6 and 4 to get 24.

$$24\sqrt{20}$$

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}.

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

Multiply 24 and 2 to get 48.

$$48\sqrt{5}$$