Solve sqrt{2/5}*sqrt{50}-sqrt{45}

$$\sqrt { \frac { 2 } { 5 } } \times \sqrt { 50 } - \sqrt { 45 }$$

Evaluate

$$-\sqrt{5}\approx -2.236067977$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{2}{5}} as the division of square roots \frac{\sqrt{2}}{\sqrt{5}}.

$$\frac{\sqrt{2}}{\sqrt{5}}\sqrt{50}-\sqrt{45}$$

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

$$\frac{\sqrt{2}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\sqrt{50}-\sqrt{45}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{2}\sqrt{5}}{5}\sqrt{50}-\sqrt{45}$$

To multiply \sqrt{2} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{\sqrt{10}}{5}\sqrt{50}-\sqrt{45}$$

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}.

$$\frac{\sqrt{10}}{5}\times 5\sqrt{2}-\sqrt{45}$$

Cancel out 5 and 5.

$$\sqrt{10}\sqrt{2}-\sqrt{45}$$

Factor 10=2\times 5. Rewrite the square root of the product \sqrt{2\times 5} as the product of square roots \sqrt{2}\sqrt{5}.

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

Multiply \sqrt{2} and \sqrt{2} to get 2.

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

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

$$2\sqrt{5}-3\sqrt{5}$$

Combine 2\sqrt{5} and -3\sqrt{5} to get -\sqrt{5}.

$$-\sqrt{5}$$