Solve 2sqrt{6}(3sqrt{2}-1/4sqrt{12})

$$2 \sqrt { 6 } ( 3 \sqrt { 2 } - \frac { 1 } { 4 } \sqrt { 12 } )$$

Evaluate

$$12\sqrt{3}-3\sqrt{2}\approx 16.541969004$$

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}.

$$2\sqrt{6}\left(3\sqrt{2}-\frac{1}{4}\times 2\sqrt{3}\right)$$

Express -\frac{1}{4}\times 2 as a single fraction.

$$2\sqrt{6}\left(3\sqrt{2}+\frac{-2}{4}\sqrt{3}\right)$$

Reduce the fraction \frac{-2}{4} to lowest terms by extracting and canceling out 2.

$$2\sqrt{6}\left(3\sqrt{2}-\frac{1}{2}\sqrt{3}\right)$$

Use the distributive property to multiply 2\sqrt{6} by 3\sqrt{2}-\frac{1}{2}\sqrt{3}.

$$6\sqrt{6}\sqrt{2}+2\sqrt{6}\left(-\frac{1}{2}\right)\sqrt{3}$$

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

$$6\sqrt{2}\sqrt{3}\sqrt{2}+2\sqrt{6}\left(-\frac{1}{2}\right)\sqrt{3}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$6\times 2\sqrt{3}+2\sqrt{6}\left(-\frac{1}{2}\right)\sqrt{3}$$

Multiply 6 and 2 to get 12.

$$12\sqrt{3}+2\sqrt{6}\left(-\frac{1}{2}\right)\sqrt{3}$$

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

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

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

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

Multiply 2 and 3 to get 6.

$$12\sqrt{3}+6\left(-\frac{1}{2}\right)\sqrt{2}$$

Express 6\left(-\frac{1}{2}\right) as a single fraction.

$$12\sqrt{3}+\frac{6\left(-1\right)}{2}\sqrt{2}$$

Multiply 6 and -1 to get -6.

$$12\sqrt{3}+\frac{-6}{2}\sqrt{2}$$

Divide -6 by 2 to get -3.

$$12\sqrt{3}-3\sqrt{2}$$

Factor

$$3 {(4 \sqrt{3} - \sqrt{2})} = 16.541969004$$