Solve 2sqrt{8}-4sqrt{32}

$$2 \sqrt { 8 } - 4 \sqrt { 32 }$$

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}.

$$2\times 2\sqrt{2}-4\sqrt{32}$$

Multiply 2 and 2 to get 4.

$$4\sqrt{2}-4\sqrt{32}$$

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}.

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

Multiply -4 and 4 to get -16.

$$4\sqrt{2}-16\sqrt{2}$$

Combine 4\sqrt{2} and -16\sqrt{2} to get -12\sqrt{2}.

$$-12\sqrt{2}$$