Solve 4div1/2*1/sqrt{2}

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

Evaluate

$$4\sqrt{2}\approx 5.656854249$$

Solution Steps

Divide 4 by \frac{1}{2} by multiplying 4 by the reciprocal of \frac{1}{2}.

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

Multiply 4 and 2 to get 8.

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

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

$$8\times \frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$8\times \frac{\sqrt{2}}{2}$$

Cancel out 2, the greatest common factor in 8 and 2.

$$4\sqrt{2}$$