Solve sqrt{50}+sqrt{512}+5sqrt{2}

$$\sqrt { 50 } + \sqrt { 512 } + 5 \sqrt { 2 }$$

Evaluate

$$26\sqrt{2}\approx 36.769552622$$

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}.

$$5\sqrt{2}+\sqrt{512}+5\sqrt{2}$$

Factor 512=16^{2}\times 2. Rewrite the square root of the product \sqrt{16^{2}\times 2} as the product of square roots \sqrt{16^{2}}\sqrt{2}. Take the square root of 16^{2}.

$$5\sqrt{2}+16\sqrt{2}+5\sqrt{2}$$

Combine 5\sqrt{2} and 16\sqrt{2} to get 21\sqrt{2}.

$$21\sqrt{2}+5\sqrt{2}$$

Combine 21\sqrt{2} and 5\sqrt{2} to get 26\sqrt{2}.

$$26\sqrt{2}$$