Solve sqrt{48}+sqrt{75}-sqrt{108}

$$\sqrt{ 48 } + \sqrt{ 75 } - \sqrt{ 108 }$$

Evaluate

$$3\sqrt{3}\approx 5.196152423$$

Solution Steps

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$4\sqrt{3}+\sqrt{75}-\sqrt{108}$$

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}.

$$4\sqrt{3}+5\sqrt{3}-\sqrt{108}$$

Combine 4\sqrt{3} and 5\sqrt{3} to get 9\sqrt{3}.

$$9\sqrt{3}-\sqrt{108}$$

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}.

$$9\sqrt{3}-6\sqrt{3}$$

Combine 9\sqrt{3} and -6\sqrt{3} to get 3\sqrt{3}.

$$3\sqrt{3}$$