Solve sqrt{8}+sqrt{18}+sqrt{32}+sqrt{50}=

$$\sqrt { 8 } + \sqrt { 18 } + \sqrt { 32 } + \sqrt { 50 } =$$

Evaluate

$$14\sqrt{2}\approx 19.798989873$$

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}.

$$2\sqrt{2}+\sqrt{18}+\sqrt{32}+\sqrt{50}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$2\sqrt{2}+3\sqrt{2}+\sqrt{32}+\sqrt{50}$$

Combine 2\sqrt{2} and 3\sqrt{2} to get 5\sqrt{2}.

$$5\sqrt{2}+\sqrt{32}+\sqrt{50}$$

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$5\sqrt{2}+4\sqrt{2}+\sqrt{50}$$

Combine 5\sqrt{2} and 4\sqrt{2} to get 9\sqrt{2}.

$$9\sqrt{2}+\sqrt{50}$$

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}.

$$9\sqrt{2}+5\sqrt{2}$$

Combine 9\sqrt{2} and 5\sqrt{2} to get 14\sqrt{2}.

$$14\sqrt{2}$$