Solve sqrt{12}-sqrt{48}+sqrt{300}

$$\sqrt { 12 } - \sqrt { 48 } + \sqrt { 300 }$$

Evaluate

$$8\sqrt{3}\approx 13.856406461$$

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}.

$$2\sqrt{3}-\sqrt{48}+\sqrt{300}$$

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}.

$$2\sqrt{3}-4\sqrt{3}+\sqrt{300}$$

Combine 2\sqrt{3} and -4\sqrt{3} to get -2\sqrt{3}.

$$-2\sqrt{3}+\sqrt{300}$$

Factor 300=10^{2}\times 3. Rewrite the square root of the product \sqrt{10^{2}\times 3} as the product of square roots \sqrt{10^{2}}\sqrt{3}. Take the square root of 10^{2}.

$$-2\sqrt{3}+10\sqrt{3}$$

Combine -2\sqrt{3} and 10\sqrt{3} to get 8\sqrt{3}.

$$8\sqrt{3}$$