Solve 10(1/2)/1/2sqrt{2}=

$$\frac { 10 ( 1 / 2 ) } { 1 / 2 \sqrt { 2 } } =$$

Evaluate

$$5\sqrt{2}\approx 7.071067812$$

Solution Steps

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{10}{\sqrt{2}\times \left(\frac{1}{2}\right)^{0}}$$

Calculate \frac{1}{2} to the power of 0 and get 1.

$$\frac{10}{\sqrt{2}\times 1}$$

Rationalize the denominator of \frac{10}{\sqrt{2}\times 1} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

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

Divide 10\sqrt{2} by 2 to get 5\sqrt{2}.

$$5\sqrt{2}$$