Solve 6sqrt{8}-sqrt{32}

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

Evaluate

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

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}.

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

Multiply 6 and 2 to get 12.

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

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}.

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

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

$$8\sqrt{2}$$