Solve 1/sqrt{2}=frac{1*sqrt{2}}{sqrt{2}sqrt{2}}

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

Verify

Solution Steps

Multiply \sqrt{2} and \sqrt{2} to get 2.

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

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

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

The square of \sqrt{2} is 2.

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

Subtract \frac{1\sqrt{2}}{2} from both sides.

$$\frac{\sqrt{2}}{2}-\frac{1\sqrt{2}}{2}=0$$

Combine \frac{\sqrt{2}}{2} and -\frac{1\sqrt{2}}{2} to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$