Solve -18divsqrt{5}-20*2divsqrt{5}

$$-18 \div \sqrt{ 5 } -20 \times 2 \div \sqrt{ 5 }$$

Evaluate

$$-\frac{58\sqrt{5}}{5}\approx -25.938388539$$

Solution Steps

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

$$\frac{-18\sqrt{5}}{\left(\sqrt{5}\right)^{2}}-\frac{20\times 2}{\sqrt{5}}$$

The square of \sqrt{5} is 5.

$$\frac{-18\sqrt{5}}{5}-\frac{20\times 2}{\sqrt{5}}$$

Multiply 20 and 2 to get 40.

$$\frac{-18\sqrt{5}}{5}-\frac{40}{\sqrt{5}}$$

Rationalize the denominator of \frac{40}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{-18\sqrt{5}}{5}-\frac{40\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{-18\sqrt{5}}{5}-\frac{40\sqrt{5}}{5}$$

Divide 40\sqrt{5} by 5 to get 8\sqrt{5}.

$$\frac{-18\sqrt{5}}{5}-8\sqrt{5}$$

Combine \frac{-18\sqrt{5}}{5} and -8\sqrt{5} to get -\frac{58}{5}\sqrt{5}.

$$-\frac{58}{5}\sqrt{5}$$