Solve 16sqrt{8}-12sqrt{32}+56

$$16 \sqrt { 8 } - 12 \sqrt { 32 } + 56$$

Evaluate

$$56-16\sqrt{2}\approx 33.372583002$$

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}.

$$16\times 2\sqrt{2}-12\sqrt{32}+56$$

Multiply 16 and 2 to get 32.

$$32\sqrt{2}-12\sqrt{32}+56$$

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}.

$$32\sqrt{2}-12\times 4\sqrt{2}+56$$

Multiply -12 and 4 to get -48.

$$32\sqrt{2}-48\sqrt{2}+56$$

Combine 32\sqrt{2} and -48\sqrt{2} to get -16\sqrt{2}.

$$-16\sqrt{2}+56$$

Factor

$$8 {(7 - 2 \sqrt{2})} = 33.372583002$$