Solve 2/2-(1/6sqrt{24}-3/8sqrt{12})

$$\frac { 2 } { 2 } - ( \frac { 1 } { 6 } \sqrt { 24 } - \frac { 3 } { 8 } \sqrt { 12 } )$$

Evaluate

$$\frac{3\sqrt{3}}{4}-\frac{\sqrt{6}}{3}+1\approx 1.482541525$$

Solution Steps

Divide 2 by 2 to get 1.

$$1-\left(\frac{1}{6}\sqrt{24}-\frac{3}{8}\sqrt{12}\right)$$

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$1-\left(\frac{1}{6}\times 2\sqrt{6}-\frac{3}{8}\sqrt{12}\right)$$

Multiply \frac{1}{6} and 2 to get \frac{2}{6}.

$$1-\left(\frac{2}{6}\sqrt{6}-\frac{3}{8}\sqrt{12}\right)$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$1-\left(\frac{1}{3}\sqrt{6}-\frac{3}{8}\sqrt{12}\right)$$

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}.

$$1-\left(\frac{1}{3}\sqrt{6}-\frac{3}{8}\times 2\sqrt{3}\right)$$

Express -\frac{3}{8}\times 2 as a single fraction.

$$1-\left(\frac{1}{3}\sqrt{6}+\frac{-3\times 2}{8}\sqrt{3}\right)$$

Multiply -3 and 2 to get -6.

$$1-\left(\frac{1}{3}\sqrt{6}+\frac{-6}{8}\sqrt{3}\right)$$

Reduce the fraction \frac{-6}{8} to lowest terms by extracting and canceling out 2.

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

To find the opposite of \frac{1}{3}\sqrt{6}-\frac{3}{4}\sqrt{3}, find the opposite of each term.

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

The opposite of -\frac{3}{4}\sqrt{3} is \frac{3}{4}\sqrt{3}.

$$1-\frac{1}{3}\sqrt{6}+\frac{3}{4}\sqrt{3}$$

Factor

$$\frac{9 \sqrt{3} + 12 - 4 \sqrt{6}}{12} = 1.482541524748932$$