Solve 10sqrt{1/2}

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

Evaluate

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

Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{2}} as the division of square roots \frac{\sqrt{1}}{\sqrt{2}}.

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

Calculate the square root of 1 and get 1.

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

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

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

The square of \sqrt{2} is 2.

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

Cancel out 2, the greatest common factor in 10 and 2.

$$5\sqrt{2}$$