Solve 2sqrt{50}-5sqrt{32}+5sqrt{8}

$$2 \sqrt { 50 } - 5 \sqrt { 32 } + 5 \sqrt { 8 }$$

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}.

$$2\times 5\sqrt{2}-5\sqrt{32}+5\sqrt{8}$$

Multiply 2 and 5 to get 10.

$$10\sqrt{2}-5\sqrt{32}+5\sqrt{8}$$

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}.

$$10\sqrt{2}-5\times 4\sqrt{2}+5\sqrt{8}$$

Multiply -5 and 4 to get -20.

$$10\sqrt{2}-20\sqrt{2}+5\sqrt{8}$$

Combine 10\sqrt{2} and -20\sqrt{2} to get -10\sqrt{2}.

$$-10\sqrt{2}+5\sqrt{8}$$

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}.

$$-10\sqrt{2}+5\times 2\sqrt{2}$$

Multiply 5 and 2 to get 10.

$$-10\sqrt{2}+10\sqrt{2}$$

Combine -10\sqrt{2} and 10\sqrt{2} to get 0.

$$0$$

Factor

$$0$$