Solve sqrt{32}+2sqrt{10}+5sqrt{3}-sqrt{72}

$$\sqrt{ 32 } +2 \sqrt{ 10 } +5 \sqrt{ 3 } - \sqrt{ 72 }$$

Evaluate

$$2\sqrt{10}+5\sqrt{3}-2\sqrt{2}\approx 12.156382233$$

Solution Steps

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}.

$$4\sqrt{2}+2\sqrt{10}+5\sqrt{3}-\sqrt{72}$$

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$4\sqrt{2}+2\sqrt{10}+5\sqrt{3}-6\sqrt{2}$$

Combine 4\sqrt{2} and -6\sqrt{2} to get -2\sqrt{2}.

$$-2\sqrt{2}+2\sqrt{10}+5\sqrt{3}$$