Solve 1/2-frac{sqrt{32}}{4}+3/6

$$\frac { 1 } { 2 } - \frac { \sqrt { 32 } } { 4 } + \frac { 3 } { 6 }$$

Evaluate

$$1-\sqrt{2}\approx -0.414213562$$

Solution Steps

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$\frac{1}{2}-\frac{4\sqrt{2}}{4}+\frac{3}{6}$$

Cancel out 4 and 4.

$$\frac{1}{2}-\sqrt{2}+\frac{3}{6}$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{1}{2}-\sqrt{2}+\frac{1}{2}$$

Since \frac{1}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$\frac{1+1}{2}-\sqrt{2}$$

Add 1 and 1 to get 2.

$$\frac{2}{2}-\sqrt{2}$$

Divide 2 by 2 to get 1.

$$1-\sqrt{2}$$

Factor

$$1-\sqrt{2}$$