Solve sqrt{28}+sqrt{175}+sqrt{252}

$$\sqrt { 28 } + \sqrt { 175 } + \sqrt { 252 }$$

Evaluate

$$13\sqrt{7}\approx 34.394767044$$

Solution Steps

Factor 28=2^{2}\times 7. Rewrite the square root of the product \sqrt{2^{2}\times 7} as the product of square roots \sqrt{2^{2}}\sqrt{7}. Take the square root of 2^{2}.

$$2\sqrt{7}+\sqrt{175}+\sqrt{252}$$

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}.

$$2\sqrt{7}+5\sqrt{7}+\sqrt{252}$$

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

$$7\sqrt{7}+\sqrt{252}$$

Factor 252=6^{2}\times 7. Rewrite the square root of the product \sqrt{6^{2}\times 7} as the product of square roots \sqrt{6^{2}}\sqrt{7}. Take the square root of 6^{2}.

$$7\sqrt{7}+6\sqrt{7}$$

Combine 7\sqrt{7} and 6\sqrt{7} to get 13\sqrt{7}.

$$13\sqrt{7}$$