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

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

Evaluate

$$-1$$

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}.

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

Rationalize the denominator of \frac{4}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

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

Divide 4\sqrt{2} by 2 to get 2\sqrt{2}.

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

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

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

Calculate the square root of 4 and get 2.

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

Subtract 2\sqrt{2} from 2\sqrt{2} to get 0.

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

Calculate \frac{1}{3} to the power of -1 and get 3.

$$2-3$$

Subtract 3 from 2 to get -1.

$$-1$$

Factor

$$-1$$