Solve 3sqrt{8}-sqrt{2}+sqrt{32}

$$3 \sqrt{ 8 } - \sqrt{ 2 } + \sqrt{ 32 }$$

Evaluate

$$9\sqrt{2}\approx 12.727922061$$

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}.

$$3\times 2\sqrt{2}-\sqrt{2}+\sqrt{32}$$

Multiply 3 and 2 to get 6.

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

Combine 6\sqrt{2} and -\sqrt{2} to get 5\sqrt{2}.

$$5\sqrt{2}+\sqrt{32}$$

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}.

$$5\sqrt{2}+4\sqrt{2}$$

Combine 5\sqrt{2} and 4\sqrt{2} to get 9\sqrt{2}.

$$9\sqrt{2}$$