Solve sqrt{12}-sqrt{27}+sqrt{3}=0

$$\sqrt { 12 } - \sqrt { 27 } + \sqrt { 3 } = 0$$

Verify

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}.

$$2\sqrt{3}-\sqrt{27}+\sqrt{3}=0$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$2\sqrt{3}-3\sqrt{3}+\sqrt{3}=0$$

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

$$-\sqrt{3}+\sqrt{3}=0$$

Combine -\sqrt{3} and \sqrt{3} to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$