Solve -45/2sqrt{20}

$$\frac { - 45 } { 2 \sqrt { 20 } }$$

Evaluate

$$-\frac{9\sqrt{5}}{4}\approx -5.031152949$$

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}.

$$\frac{-45}{2\times 2\sqrt{5}}$$

Multiply 2 and 2 to get 4.

$$\frac{-45}{4\sqrt{5}}$$

Rationalize the denominator of \frac{-45}{4\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{-45\sqrt{5}}{4\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{-45\sqrt{5}}{4\times 5}$$

Cancel out 5 in both numerator and denominator.

$$\frac{-9\sqrt{5}}{4}$$