Solve sqrt{108}-sqrt{75}

$$\sqrt{ 108 } - \sqrt{ 75 }$$

Evaluate

$$\sqrt{3}\approx 1.732050808$$

Solution Steps

Factor 108=6^{2}\times 3. Rewrite the square root of the product \sqrt{6^{2}\times 3} as the product of square roots \sqrt{6^{2}}\sqrt{3}. Take the square root of 6^{2}.

$$6\sqrt{3}-\sqrt{75}$$

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$6\sqrt{3}-5\sqrt{3}$$

Combine 6\sqrt{3} and -5\sqrt{3} to get \sqrt{3}.

$$\sqrt{3}$$