Solve 2sqrt{50}+sqrt{90}-frac{sqrt{40}}{2}

$$2 \sqrt { 50 } + \sqrt { 90 } - \frac { \sqrt { 40 } } { 2 }$$

Evaluate

$$2\left(\sqrt{10}+5\sqrt{2}\right)\approx 20.466690944$$

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}.

$$2\times 5\sqrt{2}+\sqrt{90}-\frac{\sqrt{40}}{2}$$

Multiply 2 and 5 to get 10.

$$10\sqrt{2}+\sqrt{90}-\frac{\sqrt{40}}{2}$$

Factor 90=3^{2}\times 10. Rewrite the square root of the product \sqrt{3^{2}\times 10} as the product of square roots \sqrt{3^{2}}\sqrt{10}. Take the square root of 3^{2}.

$$10\sqrt{2}+3\sqrt{10}-\frac{\sqrt{40}}{2}$$

Factor 40=2^{2}\times 10. Rewrite the square root of the product \sqrt{2^{2}\times 10} as the product of square roots \sqrt{2^{2}}\sqrt{10}. Take the square root of 2^{2}.

$$10\sqrt{2}+3\sqrt{10}-\frac{2\sqrt{10}}{2}$$

Cancel out 2 and 2.

$$10\sqrt{2}+3\sqrt{10}-\sqrt{10}$$

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

$$10\sqrt{2}+2\sqrt{10}$$

Factor

$$2 {(\sqrt{10} + 5 \sqrt{2})} = 20.466690944$$