Solve 2sqrt{75}*sqrt{12}=

$$2 \sqrt { 75 } \times \sqrt { 12 } =$$

Evaluate

$$60$$

Solution Steps

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$2\times 5\sqrt{3}\sqrt{12}$$

Multiply 2 and 5 to get 10.

$$10\sqrt{3}\sqrt{12}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$10\sqrt{3}\times 2\sqrt{3}$$

Multiply 10 and 2 to get 20.

$$20\sqrt{3}\sqrt{3}$$

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

$$20\times 3$$

Multiply 20 and 3 to get 60.

$$60$$

Factor

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