Solve sqrt{50}-2sqrt{32}+3sqrt{2}

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

Evaluate

$$0$$

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}.

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

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}.

$$5\sqrt{2}-2\times 4\sqrt{2}+3\sqrt{2}$$

Multiply -2 and 4 to get -8.

$$5\sqrt{2}-8\sqrt{2}+3\sqrt{2}$$

Combine 5\sqrt{2} and -8\sqrt{2} to get -3\sqrt{2}.

$$-3\sqrt{2}+3\sqrt{2}$$

Combine -3\sqrt{2} and 3\sqrt{2} to get 0.

$$0$$

Factor

$$0$$