Solve 5sqrt{2}divfrac{sqrt{2}}{2}

$$5 \sqrt{ 2 } \div \frac{ \sqrt{ 2 } }{ 2 }$$

Evaluate

$$10$$

Solution Steps

Divide 5\sqrt{2} by \frac{\sqrt{2}}{2} by multiplying 5\sqrt{2} by the reciprocal of \frac{\sqrt{2}}{2}.

$$\frac{5\sqrt{2}\times 2}{\sqrt{2}}$$

Multiply 5 and 2 to get 10.

$$\frac{10\sqrt{2}}{\sqrt{2}}$$

Rationalize the denominator of \frac{10\sqrt{2}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{10\sqrt{2}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{10\sqrt{2}\sqrt{2}}{2}$$

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

$$\frac{10\times 2}{2}$$

Multiply 10 and 2 to get 20.

$$\frac{20}{2}$$

Divide 20 by 2 to get 10.

$$10$$

Factor

$$2\times 5$$