Solve sqrt{50}-frac{sqrt{100}}{sqrt{4}}

$$\sqrt { 50 } - \frac { \sqrt { 100 } } { \sqrt { 4 } }$$

Evaluate

$$5\left(\sqrt{2}-1\right)\approx 2.071067812$$

Solution Steps

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}.

$$5\sqrt{2}-\frac{\sqrt{100}}{\sqrt{4}}$$

Rewrite the division of square roots \frac{\sqrt{100}}{\sqrt{4}} as the square root of the division \sqrt{\frac{100}{4}} and perform the division.

$$5\sqrt{2}-\sqrt{25}$$

Calculate the square root of 25 and get 5.

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