Solve 3/10sqrt{10}*2/5sqrt{5}+frac{-sqrt{50}}{50}

$$\frac { 3 } { 10 } \sqrt { 10 } \times \frac { 2 } { 5 } \sqrt { 5 } + \frac { - \sqrt { 50 } } { 50 }$$

Evaluate

$$\frac{\sqrt{2}}{2}\approx 0.707106781$$

Solution Steps

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

$$\frac{3}{10}\sqrt{5}\sqrt{2}\times \frac{2}{5}\sqrt{5}+\frac{-\sqrt{50}}{50}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$\frac{3}{10}\times 5\times \frac{2}{5}\sqrt{2}+\frac{-\sqrt{50}}{50}$$

Express \frac{3}{10}\times 5 as a single fraction.

$$\frac{3\times 5}{10}\times \frac{2}{5}\sqrt{2}+\frac{-\sqrt{50}}{50}$$

Multiply 3 and 5 to get 15.

$$\frac{15}{10}\times \frac{2}{5}\sqrt{2}+\frac{-\sqrt{50}}{50}$$

Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.

$$\frac{3}{2}\times \frac{2}{5}\sqrt{2}+\frac{-\sqrt{50}}{50}$$

Multiply \frac{3}{2} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 2}{2\times 5}\sqrt{2}+\frac{-\sqrt{50}}{50}$$

Cancel out 2 in both numerator and denominator.

$$\frac{3}{5}\sqrt{2}+\frac{-\sqrt{50}}{50}$$

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}.

$$\frac{3}{5}\sqrt{2}+\frac{-5\sqrt{2}}{50}$$

Divide -5\sqrt{2} by 50 to get -\frac{1}{10}\sqrt{2}.

$$\frac{3}{5}\sqrt{2}-\frac{1}{10}\sqrt{2}$$

Combine \frac{3}{5}\sqrt{2} and -\frac{1}{10}\sqrt{2} to get \frac{1}{2}\sqrt{2}.

$$\frac{1}{2}\sqrt{2}$$