Solve {l}{2*7}{(3-sqrt{6})(3+sqrt{6})}

$$\left. \begin{array} { l } { 2 \times 7 } \\ { ( 3 - \sqrt { 6 } ) ( 3 + \sqrt { 6 } ) } \end{array} \right.$$

Sort

$$3,14$$

Solution Steps

Multiply 2 and 7 to get 14.

$$sort(14,\left(3-\sqrt{6}\right)\left(3+\sqrt{6}\right))$$

Consider \left(3-\sqrt{6}\right)\left(3+\sqrt{6}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$sort(14,3^{2}-\left(\sqrt{6}\right)^{2})$$

Calculate 3 to the power of 2 and get 9.

$$sort(14,9-\left(\sqrt{6}\right)^{2})$$

The square of \sqrt{6} is 6.

$$sort(14,9-6)$$

Subtract 6 from 9 to get 3.

$$sort(14,3)$$

To sort the list, start from a single element 14.

$$14$$

Insert 3 to the appropriate location in the new list.

$$3,14$$

Evaluate

$$14,\ 3$$