Solve sqrt{8}-4/12+sqrt{(-2)^2}-(1/3)

$$\sqrt { 8 } - \frac { 4 } { 12 } + \sqrt { ( - 2 ) ^ { 2 } } - ( \frac { 1 } { 3 } )$$

Evaluate

$$2\sqrt{2}+\frac{4}{3}\approx 4.161760458$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$2\sqrt{2}-\frac{4}{12}+\sqrt{\left(-2\right)^{2}}-\frac{1}{3}$$

Reduce the fraction \frac{4}{12} to lowest terms by extracting and canceling out 4.

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

Calculate -2 to the power of 2 and get 4.

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

Calculate the square root of 4 and get 2.

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

Convert 2 to fraction \frac{6}{3}.

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

Since -\frac{1}{3} and \frac{6}{3} have the same denominator, add them by adding their numerators.

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

Add -1 and 6 to get 5.

$$2\sqrt{2}+\frac{5}{3}-\frac{1}{3}$$

Since \frac{5}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$2\sqrt{2}+\frac{5-1}{3}$$

Subtract 1 from 5 to get 4.

$$2\sqrt{2}+\frac{4}{3}$$

Factor

$$\frac{2 \sqrt{2} {(\sqrt{2} + 3)}}{3} = 4.161760458079524$$