Solve 1div(-9sqrt{20})

$$1 \div (-9 \sqrt{ 20 } )$$

Evaluate

$$-\frac{\sqrt{5}}{90}\approx -0.0248452$$

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}.

$$\frac{1}{-9\times 2\sqrt{5}}$$

Multiply -9 and 2 to get -18.

$$\frac{1}{-18\sqrt{5}}$$

Rationalize the denominator of \frac{1}{-18\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{5}}{-18\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{5}}{-18\times 5}$$

Multiply -18 and 5 to get -90.

$$\frac{\sqrt{5}}{-90}$$