Solve (sqrt{12}-2sqrt{75})*sqrt{3}

$$( \sqrt { 12 } - 2 \sqrt { 75 } ) \times \sqrt { 3 }$$

Evaluate

$$-24$$

Solution Steps

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}.

$$\left(2\sqrt{3}-2\sqrt{75}\right)\sqrt{3}$$

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}.

$$\left(2\sqrt{3}-2\times 5\sqrt{3}\right)\sqrt{3}$$

Multiply -2 and 5 to get -10.

$$\left(2\sqrt{3}-10\sqrt{3}\right)\sqrt{3}$$

Combine 2\sqrt{3} and -10\sqrt{3} to get -8\sqrt{3}.

$$-8\sqrt{3}\sqrt{3}$$

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

$$-8\times 3$$

Multiply -8 and 3 to get -24.

$$-24$$

Factor

$$-24$$