Solve (1/5)^-1+(1+sqrt{3})(1+sqrt{3})-sqrt{12}

$$( \frac { 1 } { 5 } ) ^ { - 1 } + ( 1 + \sqrt { 3 } ) ( 1 + \sqrt { 3 } ) - \sqrt { 12 }$$

Evaluate

$$9$$

Solution Steps

Multiply 1+\sqrt{3} and 1+\sqrt{3} to get \left(1+\sqrt{3}\right)^{2}.

$$\left(\frac{1}{5}\right)^{-1}+\left(1+\sqrt{3}\right)^{2}-\sqrt{12}$$

Calculate \frac{1}{5} to the power of -1 and get 5.

$$5+\left(1+\sqrt{3}\right)^{2}-\sqrt{12}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(1+\sqrt{3}\right)^{2}.

$$5+1+2\sqrt{3}+\left(\sqrt{3}\right)^{2}-\sqrt{12}$$

The square of \sqrt{3} is 3.

$$5+1+2\sqrt{3}+3-\sqrt{12}$$

Add 1 and 3 to get 4.

$$5+4+2\sqrt{3}-\sqrt{12}$$

Add 5 and 4 to get 9.

$$9+2\sqrt{3}-\sqrt{12}$$

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}.

$$9+2\sqrt{3}-2\sqrt{3}$$

Combine 2\sqrt{3} and -2\sqrt{3} to get 0.

$$9$$

Factor

$$3^{2}$$