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

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

Evaluate

$$12\sqrt{2}\approx 16.970562748$$

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}.

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

Multiply 2 and 2 to get 4.

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

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}.

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

Multiply -3 and 4 to get -12.

$$4\sqrt{2}-12\sqrt{2}+4\sqrt{50}$$

Combine 4\sqrt{2} and -12\sqrt{2} to get -8\sqrt{2}.

$$-8\sqrt{2}+4\sqrt{50}$$

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}.

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

Multiply 4 and 5 to get 20.

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

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

$$12\sqrt{2}$$