Solve (2-3sqrt{3})(2-3sqrt{3})

$$( 2 - 3 \sqrt { 3 } ) ( 2 - 3 \sqrt { 3 } )$$

Evaluate

$$31-12\sqrt{3}\approx 10.215390309$$

Solution Steps

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

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

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

$$4-12\sqrt{3}+9\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$4-12\sqrt{3}+9\times 3$$

Multiply 9 and 3 to get 27.

$$4-12\sqrt{3}+27$$

Add 4 and 27 to get 31.

$$31-12\sqrt{3}$$

Factor

$$31-12\sqrt{3}$$