Solve sqrt{9/20}*(-6)

$$\sqrt{ \frac{ 9 }{ 20 } } \times (-6)$$

Evaluate

$$-\frac{9\sqrt{5}}{5}\approx -4.024922359$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{9}{20}} as the division of square roots \frac{\sqrt{9}}{\sqrt{20}}.

$$\frac{\sqrt{9}}{\sqrt{20}}\left(-6\right)$$

Calculate the square root of 9 and get 3.

$$\frac{3}{\sqrt{20}}\left(-6\right)$$

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}.

$$\frac{3}{2\sqrt{5}}\left(-6\right)$$

Rationalize the denominator of \frac{3}{2\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{3\sqrt{5}}{2\left(\sqrt{5}\right)^{2}}\left(-6\right)$$

The square of \sqrt{5} is 5.

$$\frac{3\sqrt{5}}{2\times 5}\left(-6\right)$$

Multiply 2 and 5 to get 10.

$$\frac{3\sqrt{5}}{10}\left(-6\right)$$

Express \frac{3\sqrt{5}}{10}\left(-6\right) as a single fraction.

$$\frac{-3\sqrt{5}\times 6}{10}$$

Multiply -3 and 6 to get -18.

$$\frac{-18\sqrt{5}}{10}$$

Divide -18\sqrt{5} by 10 to get -\frac{9}{5}\sqrt{5}.

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