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

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

Evaluate

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

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}.

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

Multiply -2 and 5 to get -10.

$$-10\sqrt{2}+3\sqrt{8}-4\sqrt{2}$$

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}.

$$-10\sqrt{2}+3\times 2\sqrt{2}-4\sqrt{2}$$

Multiply 3 and 2 to get 6.

$$-10\sqrt{2}+6\sqrt{2}-4\sqrt{2}$$

Combine -10\sqrt{2} and 6\sqrt{2} to get -4\sqrt{2}.

$$-4\sqrt{2}-4\sqrt{2}$$

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

$$-8\sqrt{2}$$