Solve sqrt{2000}*0.5+sqrt{1000}*0.5

$$\sqrt { 2000 } \times 0.5 + \sqrt { 1000 } \times 0.5$$

Evaluate

$$5\sqrt{10}+10\sqrt{5}\approx 38.172068076$$

Solution Steps

Factor 2000=20^{2}\times 5. Rewrite the square root of the product \sqrt{20^{2}\times 5} as the product of square roots \sqrt{20^{2}}\sqrt{5}. Take the square root of 20^{2}.

$$0.5\times 20\sqrt{5}+0.5\sqrt{1000}$$

Multiply 0.5 and 20 to get 10.

$$10\sqrt{5}+0.5\sqrt{1000}$$

Factor 1000=10^{2}\times 10. Rewrite the square root of the product \sqrt{10^{2}\times 10} as the product of square roots \sqrt{10^{2}}\sqrt{10}. Take the square root of 10^{2}.

$$10\sqrt{5}+0.5\times 10\sqrt{10}$$

Multiply 0.5 and 10 to get 5.

$$10\sqrt{5}+5\sqrt{10}$$

Factor

$$\sqrt{5} \sqrt{10} {(\sqrt{5} + \sqrt{10})} = 38.172068076$$