Solve sqrt{50}-3sqrt{18}+5sqrt{32}

$$\sqrt { 50 } - 3 \sqrt { 18 } + 5 \sqrt { 32 }$$

Evaluate

$$16\sqrt{2}\approx 22.627416998$$

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}.

$$5\sqrt{2}-3\sqrt{18}+5\sqrt{32}$$

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}.

$$5\sqrt{2}-3\times 3\sqrt{2}+5\sqrt{32}$$

Multiply -3 and 3 to get -9.

$$5\sqrt{2}-9\sqrt{2}+5\sqrt{32}$$

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

$$-4\sqrt{2}+5\sqrt{32}$$

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}.

$$-4\sqrt{2}+5\times 4\sqrt{2}$$

Multiply 5 and 4 to get 20.

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

Combine -4\sqrt{2} and 20\sqrt{2} to get 16\sqrt{2}.

$$16\sqrt{2}$$