Solve left(sqrt{3}+1right)left(sqrt{3}-2right)+sqrt{12}-{left(sqrt{3}+1right)}^0

$$\left( \sqrt{ 3 } +1 \right) \left( \sqrt{ 3 } -2 \right) + \sqrt{ 12 } - { \left( \sqrt{ 3 } +1 \right) }^{ 0 }$$

Evaluate

$$\sqrt{3}\approx 1.732050808$$

Solution Steps

Use the distributive property to multiply \sqrt{3}+1 by \sqrt{3}-2 and combine like terms.

$$\left(\sqrt{3}\right)^{2}-\sqrt{3}-2+\sqrt{12}-\left(\sqrt{3}+1\right)^{0}$$

The square of \sqrt{3} is 3.

$$3-\sqrt{3}-2+\sqrt{12}-\left(\sqrt{3}+1\right)^{0}$$

Subtract 2 from 3 to get 1.

$$1-\sqrt{3}+\sqrt{12}-\left(\sqrt{3}+1\right)^{0}$$

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}.

$$1-\sqrt{3}+2\sqrt{3}-\left(\sqrt{3}+1\right)^{0}$$

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

$$1+\sqrt{3}-\left(\sqrt{3}+1\right)^{0}$$

Calculate \sqrt{3}+1 to the power of 0 and get 1.

$$1+\sqrt{3}-1$$

Subtract 1 from 1 to get 0.

$$\sqrt{3}$$