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

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

Evaluate

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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}.

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

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

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

The square of \sqrt{2} is 2.

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

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

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

Calculate -1 to the power of 2 and get 1.

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

Calculate the square root of 1 and get 1.

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

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

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Factor

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