Solve 3sqrt{2}-4sqrt{8}+5sqrt{50}-3sqrt{32}=

$$3 \sqrt { 2 } - 4 \sqrt { 8 } + 5 \sqrt { 50 } - 3 \sqrt { 32 } =$$

Evaluate

$$8\sqrt{2}\approx 11.313708499$$

Solution Steps

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}.

$$3\sqrt{2}-4\times 2\sqrt{2}+5\sqrt{50}-3\sqrt{32}$$

Multiply -4 and 2 to get -8.

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

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

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

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}.

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

Multiply 5 and 5 to get 25.

$$-5\sqrt{2}+25\sqrt{2}-3\sqrt{32}$$

Combine -5\sqrt{2} and 25\sqrt{2} to get 20\sqrt{2}.

$$20\sqrt{2}-3\sqrt{32}$$

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}.

$$20\sqrt{2}-3\times 4\sqrt{2}$$

Multiply -3 and 4 to get -12.

$$20\sqrt{2}-12\sqrt{2}$$

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

$$8\sqrt{2}$$