Solve sqrt{6*40}*sqrt{60}

$$\sqrt { 6 \cdot 40 } \cdot \sqrt { 60 }$$

Evaluate

$$120$$

Solution Steps

Multiply 6 and 40 to get 240.

$$\sqrt{240}\sqrt{60}$$

Factor 240=4^{2}\times 15. Rewrite the square root of the product \sqrt{4^{2}\times 15} as the product of square roots \sqrt{4^{2}}\sqrt{15}. Take the square root of 4^{2}.

$$4\sqrt{15}\sqrt{60}$$

Factor 60=2^{2}\times 15. Rewrite the square root of the product \sqrt{2^{2}\times 15} as the product of square roots \sqrt{2^{2}}\sqrt{15}. Take the square root of 2^{2}.

$$4\sqrt{15}\times 2\sqrt{15}$$

Multiply 4 and 2 to get 8.

$$8\sqrt{15}\sqrt{15}$$

Multiply \sqrt{15} and \sqrt{15} to get 15.

$$8\times 15$$

Multiply 8 and 15 to get 120.

$$120$$

Factor

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