\((2 \sqrt{5} + 3 \sqrt{7} )^2 \\ \\ (2 \sqrt{5} ) ^2 + 2 \times 2 \sqrt{5} \times 3 \sqrt{7} + (3 \sqrt{7} ^2 \\ \\ 2^2 \sqrt{5} ^2 + 2 \times 2 \sqrt{5} \times 3 \sqrt{7} + (3 \sqrt{7} )^2 \\ \\ 4 \sqrt{5} ^2 + 2 \times 2 \sqrt{5} \times 3 \sqrt{7} + (3 \sqrt{7} )^2 \\ \\ 4 \times 5 + 2 \times 2 \sqrt{5} \times 3 \sqrt{7} + (3 \sqrt{7} )^2 \\ \\ 4 \times 5 + 2 \times 2 \sqrt{5} \times 3 \sqrt{7} + 3^2 \sqrt{7} ^2 \\ \\ 4 \times 5 + 2 \times 2 \sqrt{5} \times 3 \sqrt{7} + 9 \sqrt{7} ^2\\ \\ 4 \times 5 + 2 \times 2 \sqrt{5} \times 3 \sqrt{7} + 9 \times 7 \\ \\ 20 + 2 \times 2 \sqrt{5} \times 3 \sqrt{7} + 9 \times 7 \\ \\ 20 + 2 \times 2 \times 3 \sqrt{5 \times 7} + 9 \times 7 \\ \\ 20 + 2 \times 2 \times 3 \sqrt{35} + 9 \times 7 \\ \\ 20 + 12 \sqrt{35} + 9 \times 7 \\ \\ 20 + 12 \sqrt{35} + 63 \\ \\ 83 + 12 \sqrt{35} \\ \\\)
The answer is: 83 + 12√35.
