Solve -1/5sqrt{3/50}

$$- \frac { 1 } { 5 } \sqrt { \frac { 3 } { 50 } }$$

Evaluate

$$-\frac{\sqrt{6}}{50}\approx -0.048989795$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{3}{50}} as the division of square roots \frac{\sqrt{3}}{\sqrt{50}}.

$$-\frac{1}{5}\times \frac{\sqrt{3}}{\sqrt{50}}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$-\frac{1}{5}\times \frac{\sqrt{3}}{5\sqrt{2}}$$

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

$$-\frac{1}{5}\times \frac{\sqrt{3}\sqrt{2}}{5\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$-\frac{1}{5}\times \frac{\sqrt{3}\sqrt{2}}{5\times 2}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$-\frac{1}{5}\times \frac{\sqrt{6}}{5\times 2}$$

Multiply 5 and 2 to get 10.

$$-\frac{1}{5}\times \frac{\sqrt{6}}{10}$$

Multiply -\frac{1}{5} times \frac{\sqrt{6}}{10} by multiplying numerator times numerator and denominator times denominator.

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

Multiply 5 and 10 to get 50.

$$\frac{-\sqrt{6}}{50}$$