Solve frac{sqrt{4}}{sqrt{8}}=1/sqrt{2}

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

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Solution Steps

Calculate the square root of 4 and get 2.

$$\frac{2}{\sqrt{8}}=\frac{1}{\sqrt{2}}$$

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}.

$$\frac{2}{2\sqrt{2}}=\frac{1}{\sqrt{2}}$$

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

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

The square of \sqrt{2} is 2.

$$\frac{2\sqrt{2}}{2\times 2}=\frac{1}{\sqrt{2}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{\sqrt{2}}{2}=\frac{1}{\sqrt{2}}$$

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{2}}{2}=\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{2}}{2}=\frac{\sqrt{2}}{2}$$

Subtract \frac{\sqrt{2}}{2} from both sides.

$$\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}=0$$

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

$$0=0$$

Compare 0 and 0.

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