Solve sqrt{3}-sqrt{12}+sqrt{48}=

$$\sqrt{ 3 } - \sqrt{ 12 } + \sqrt{ 48 } =$$

Evaluate

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

Solution Steps

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}.

$$\sqrt{3}-2\sqrt{3}+\sqrt{48}$$

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

$$-\sqrt{3}+\sqrt{48}$$

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}.

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

Combine -\sqrt{3} and 4\sqrt{3} to get 3\sqrt{3}.

$$3\sqrt{3}$$