Solve sqrt{175}+sqrt{243}-sqrt{63}

$$\sqrt { 175 } + \sqrt { 243 } - \sqrt { 63 }$$

Evaluate

$$2\sqrt{7}+9\sqrt{3}\approx 20.87995989$$

Solution Steps

Factor 175=5^{2}\times 7. Rewrite the square root of the product \sqrt{5^{2}\times 7} as the product of square roots \sqrt{5^{2}}\sqrt{7}. Take the square root of 5^{2}.

$$5\sqrt{7}+\sqrt{243}-\sqrt{63}$$

Factor 243=9^{2}\times 3. Rewrite the square root of the product \sqrt{9^{2}\times 3} as the product of square roots \sqrt{9^{2}}\sqrt{3}. Take the square root of 9^{2}.

$$5\sqrt{7}+9\sqrt{3}-\sqrt{63}$$

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}.

$$5\sqrt{7}+9\sqrt{3}-3\sqrt{7}$$

Combine 5\sqrt{7} and -3\sqrt{7} to get 2\sqrt{7}.

$$2\sqrt{7}+9\sqrt{3}$$