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

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

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}.

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

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

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

The square of \sqrt{2} is 2.

$$\frac{4\sqrt{2}}{2\times 2}-1-\sqrt{2}$$

Cancel out 2\times 2 in both numerator and denominator.

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

Combine \sqrt{2} and -\sqrt{2} to get 0.

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Factor

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