Solve sqrt{8}+sqrt{72}+sqrt{104}

$$\sqrt{ 8 } + \sqrt{ 72 } + \sqrt{ 104 }$$

Evaluate

$$2\left(\sqrt{26}+4\sqrt{2}\right)\approx 21.511747526$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$2\sqrt{2}+\sqrt{72}+\sqrt{104}$$

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$2\sqrt{2}+6\sqrt{2}+\sqrt{104}$$

Combine 2\sqrt{2} and 6\sqrt{2} to get 8\sqrt{2}.

$$8\sqrt{2}+\sqrt{104}$$

Factor 104=2^{2}\times 26. Rewrite the square root of the product \sqrt{2^{2}\times 26} as the product of square roots \sqrt{2^{2}}\sqrt{26}. Take the square root of 2^{2}.

$$8\sqrt{2}+2\sqrt{26}$$