Solve sqrt{208}+sqrt{744}-sqrt{20}

$$\sqrt { 208 } + \sqrt { 744 } - \sqrt { 20 }$$

Evaluate

$$2\left(\sqrt{186}+2\sqrt{13}-\sqrt{5}\right)\approx 37.226432541$$

Solution Steps

Factor 208=4^{2}\times 13. Rewrite the square root of the product \sqrt{4^{2}\times 13} as the product of square roots \sqrt{4^{2}}\sqrt{13}. Take the square root of 4^{2}.

$$4\sqrt{13}+\sqrt{744}-\sqrt{20}$$

Factor 744=2^{2}\times 186. Rewrite the square root of the product \sqrt{2^{2}\times 186} as the product of square roots \sqrt{2^{2}}\sqrt{186}. Take the square root of 2^{2}.

$$4\sqrt{13}+2\sqrt{186}-\sqrt{20}$$

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

$$4\sqrt{13}+2\sqrt{186}-2\sqrt{5}$$