Solve 6sqrt{8}-2sqrt{32}

$$6 \sqrt { 8 } - 2 \sqrt { 32 }$$

Evaluate

$$4\sqrt{2}\approx 5.656854249$$

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}.

$$6\times 2\sqrt{2}-2\sqrt{32}$$

Multiply 6 and 2 to get 12.

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

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}.

$$12\sqrt{2}-2\times 4\sqrt{2}$$

Multiply -2 and 4 to get -8.

$$12\sqrt{2}-8\sqrt{2}$$

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

$$4\sqrt{2}$$