Solve sqrt{78}-sqrt{32}+sqrt{72}

$$\sqrt { 78 } - \sqrt { 32 } + \sqrt { 72 }$$

Evaluate

$$\sqrt{78}+2\sqrt{2}\approx 11.660187991$$

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}.

$$\sqrt{78}-4\sqrt{2}+\sqrt{72}$$

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}.

$$\sqrt{78}-4\sqrt{2}+6\sqrt{2}$$

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

$$\sqrt{78}+2\sqrt{2}$$