Solve 1/sqrt{2}*4

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

Evaluate

$$2\sqrt{2}\approx 2.828427125$$

Solution Steps

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

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

The square of \sqrt{2} is 2.

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

Cancel out 2, the greatest common factor in 4 and 2.

$$2\sqrt{2}$$