Solve 2sqrt{3}*left(sqrt{12}-3sqrt{75}right)div1/3sqrt{10}+2sqrt{3}

$$2 \sqrt{ 3 } \times \left( \sqrt{ 12 } -3 \sqrt{ 75 } \right) \div \frac{ 1 }{ 3 } \sqrt{ 10 } +2 \sqrt{ 3 }$$

Evaluate

$$2\left(\sqrt{3}-117\sqrt{10}\right)\approx -736.508870864$$

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}.

$$\frac{2\sqrt{3}\left(2\sqrt{3}-3\sqrt{75}\right)}{\frac{1}{3}}\sqrt{10}+2\sqrt{3}$$

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}.

$$\frac{2\sqrt{3}\left(2\sqrt{3}-3\times 5\sqrt{3}\right)}{\frac{1}{3}}\sqrt{10}+2\sqrt{3}$$

Multiply -3 and 5 to get -15.

$$\frac{2\sqrt{3}\left(2\sqrt{3}-15\sqrt{3}\right)}{\frac{1}{3}}\sqrt{10}+2\sqrt{3}$$

Combine 2\sqrt{3} and -15\sqrt{3} to get -13\sqrt{3}.

$$\frac{2\sqrt{3}\left(-13\right)\sqrt{3}}{\frac{1}{3}}\sqrt{10}+2\sqrt{3}$$

Multiply 2 and -13 to get -26.

$$\frac{-26\sqrt{3}\sqrt{3}}{\frac{1}{3}}\sqrt{10}+2\sqrt{3}$$

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

$$\frac{-26\times 3}{\frac{1}{3}}\sqrt{10}+2\sqrt{3}$$

Multiply -26 and 3 to get -78.

$$\frac{-78}{\frac{1}{3}}\sqrt{10}+2\sqrt{3}$$

Divide -78 by \frac{1}{3} by multiplying -78 by the reciprocal of \frac{1}{3}.

$$-78\times 3\sqrt{10}+2\sqrt{3}$$

Multiply -78 and 3 to get -234.

$$-234\sqrt{10}+2\sqrt{3}$$

Factor

$$2 {(\sqrt{3} - 117 \sqrt{10})} = -736.508870864$$