Solve sqrt{126}-sqrt{56}

$$\sqrt { 126 } - \sqrt { 56 }$$

Evaluate

$$\sqrt{14}\approx 3.741657387$$

Solution Steps

Factor 126=3^{2}\times 14. Rewrite the square root of the product \sqrt{3^{2}\times 14} as the product of square roots \sqrt{3^{2}}\sqrt{14}. Take the square root of 3^{2}.

$$3\sqrt{14}-\sqrt{56}$$

Factor 56=2^{2}\times 14. Rewrite the square root of the product \sqrt{2^{2}\times 14} as the product of square roots \sqrt{2^{2}}\sqrt{14}. Take the square root of 2^{2}.

$$3\sqrt{14}-2\sqrt{14}$$

Combine 3\sqrt{14} and -2\sqrt{14} to get \sqrt{14}.

$$\sqrt{14}$$