Solve sqrt{210}+sqrt{20}-sqrt{125}-sqrt{12}

$$\sqrt { 210 } + \sqrt { 20 } - \sqrt { 125 } - \sqrt { 12 }$$

Evaluate

$$\sqrt{210}-2\sqrt{3}-3\sqrt{5}\approx 4.319071199$$

Solution Steps

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$\sqrt{210}+2\sqrt{5}-\sqrt{125}-\sqrt{12}$$

Factor 125=5^{2}\times 5. Rewrite the square root of the product \sqrt{5^{2}\times 5} as the product of square roots \sqrt{5^{2}}\sqrt{5}. Take the square root of 5^{2}.

$$\sqrt{210}+2\sqrt{5}-5\sqrt{5}-\sqrt{12}$$

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

$$\sqrt{210}-3\sqrt{5}-\sqrt{12}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\sqrt{210}-3\sqrt{5}-2\sqrt{3}$$