Solve (sqrt{12}-2sqrt{27}+3sqrt{75})*sqrt{3}

$$( \sqrt { 12 } - 2 \sqrt { 27 } + 3 \sqrt { 75 } ) \cdot \sqrt { 3 }$$

Evaluate

$$33$$

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}.

$$\left(2\sqrt{3}-2\sqrt{27}+3\sqrt{75}\right)\sqrt{3}$$

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}.

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

Multiply -2 and 3 to get -6.

$$\left(2\sqrt{3}-6\sqrt{3}+3\sqrt{75}\right)\sqrt{3}$$

Combine 2\sqrt{3} and -6\sqrt{3} to get -4\sqrt{3}.

$$\left(-4\sqrt{3}+3\sqrt{75}\right)\sqrt{3}$$

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}.

$$\left(-4\sqrt{3}+3\times 5\sqrt{3}\right)\sqrt{3}$$

Multiply 3 and 5 to get 15.

$$\left(-4\sqrt{3}+15\sqrt{3}\right)\sqrt{3}$$

Combine -4\sqrt{3} and 15\sqrt{3} to get 11\sqrt{3}.

$$11\sqrt{3}\sqrt{3}$$

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

$$11\times 3$$

Multiply 11 and 3 to get 33.

$$33$$

Factor

$$3\times 11$$