Solve 8sqrt{2}-5sqrt{32}+7sqrt{8}-3sqrt{50}=

$$8 \sqrt { 2 } - 5 \sqrt { 32 } + 7 \sqrt { 8 } - 3 \sqrt { 50 } =$$

Evaluate

$$-13\sqrt{2}\approx -18.384776311$$

Solution Steps

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}.

$$8\sqrt{2}-5\times 4\sqrt{2}+7\sqrt{8}-3\sqrt{50}$$

Multiply -5 and 4 to get -20.

$$8\sqrt{2}-20\sqrt{2}+7\sqrt{8}-3\sqrt{50}$$

Combine 8\sqrt{2} and -20\sqrt{2} to get -12\sqrt{2}.

$$-12\sqrt{2}+7\sqrt{8}-3\sqrt{50}$$

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}.

$$-12\sqrt{2}+7\times 2\sqrt{2}-3\sqrt{50}$$

Multiply 7 and 2 to get 14.

$$-12\sqrt{2}+14\sqrt{2}-3\sqrt{50}$$

Combine -12\sqrt{2} and 14\sqrt{2} to get 2\sqrt{2}.

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

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}.

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

Multiply -3 and 5 to get -15.

$$2\sqrt{2}-15\sqrt{2}$$

Combine 2\sqrt{2} and -15\sqrt{2} to get -13\sqrt{2}.

$$-13\sqrt{2}$$