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

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

Evaluate

$$\sqrt{2}\approx 1.414213562$$

Solution Steps

Combine 2\sqrt{2} and 3\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 \sqrt{2}.

$$\sqrt{2}$$