Solve sqrt{5}-sqrt{20}-sqrt{7}+sqrt{32}

$$\sqrt { 5 } - \sqrt { 20 } - \sqrt { 7 } + \sqrt { 32 }$$

Evaluate

$$4\sqrt{2}-\sqrt{5}-\sqrt{7}\approx 0.775034961$$

Solution Steps

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$\sqrt{5}-2\sqrt{5}-\sqrt{7}+\sqrt{32}$$

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

$$-\sqrt{5}-\sqrt{7}+\sqrt{32}$$

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}.

$$-\sqrt{5}-\sqrt{7}+4\sqrt{2}$$