Solve (sqrt{3}-sqrt{12})^2-1

$$( \sqrt { 3 } - \sqrt { 12 } ) ^ { 2 } - 1$$

Evaluate

$$2$$

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}.

$$\left(\sqrt{3}-2\sqrt{3}\right)^{2}-1$$

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

$$\left(-\sqrt{3}\right)^{2}-1$$

Expand \left(-\sqrt{3}\right)^{2}.

$$\left(-1\right)^{2}\left(\sqrt{3}\right)^{2}-1$$

Calculate -1 to the power of 2 and get 1.

$$1\left(\sqrt{3}\right)^{2}-1$$

The square of \sqrt{3} is 3.

$$1\times 3-1$$

Multiply 1 and 3 to get 3.

$$3-1$$

Subtract 1 from 3 to get 2.

$$2$$

Factor

$$2$$