Solve 5/sqrt{20}

$$\frac { 5 } { \sqrt { 20 } }$$

Evaluate

$$\frac{\sqrt{5}}{2}\approx 1.118033989$$

Solution Steps

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

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

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

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

The square of \sqrt{5} is 5.

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

Cancel out 5 in both numerator and denominator.

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