Solve sqrt{48}+sqrt{108}

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

Evaluate

$$10\sqrt{3}\approx 17.320508076$$

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}.

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

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}.

$$4\sqrt{3}+6\sqrt{3}$$

Combine 4\sqrt{3} and 6\sqrt{3} to get 10\sqrt{3}.

$$10\sqrt{3}$$