Solve 20*5/2sqrt{10}

$$20 \cdot \frac { 5 } { 2 \sqrt { 10 } }$$

Evaluate

$$5\sqrt{10}\approx 15.811388301$$

Solution Steps

Rationalize the denominator of \frac{5}{2\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$20\times \frac{5\sqrt{10}}{2\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$20\times \frac{5\sqrt{10}}{2\times 10}$$

Cancel out 5 in both numerator and denominator.

$$20\times \frac{\sqrt{10}}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$20\times \frac{\sqrt{10}}{4}$$

Cancel out 4, the greatest common factor in 20 and 4.

$$5\sqrt{10}$$