Solve sqrt{50}+sqrt{63}-sqrt{32}

$$\sqrt { 50 } + \sqrt { 63 } - \sqrt { 32 }$$

Evaluate

$$\sqrt{2}+3\sqrt{7}\approx 9.351467496$$

Solution Steps

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$5\sqrt{2}+\sqrt{63}-\sqrt{32}$$

Factor 63=3^{2}\times 7. Rewrite the square root of the product \sqrt{3^{2}\times 7} as the product of square roots \sqrt{3^{2}}\sqrt{7}. Take the square root of 3^{2}.

$$5\sqrt{2}+3\sqrt{7}-\sqrt{32}$$

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}.

$$5\sqrt{2}+3\sqrt{7}-4\sqrt{2}$$

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

$$\sqrt{2}+3\sqrt{7}$$