Question

(2√5 + 3√7)^2 show your work and justify each step. Thank you!

Answer 1

$(2 \sqrt{5} + 3 \sqrt{7} )^2 \\ \\ (2 \sqrt{5} ) ^2 + 2 \times 2 \sqrt{5} \times 3 \sqrt{7} + (3 \sqrt{7} ^2 \\ \\ 2^2 \sqrt{5} ^2 + 2 \times 2 \sqrt{5} \times 3 \sqrt{7} + (3 \sqrt{7} )^2 \\ \\ 4 \sqrt{5} ^2 + 2 \times 2 \sqrt{5} \times 3 \sqrt{7} + (3 \sqrt{7} )^2 \\ \\ 4 \times 5 + 2 \times 2 \sqrt{5} \times 3 \sqrt{7} + (3 \sqrt{7} )^2 \\ \\ 4 \times 5 + 2 \times 2 \sqrt{5} \times 3 \sqrt{7} + 3^2 \sqrt{7} ^2 \\ \\ 4 \times 5 + 2 \times 2 \sqrt{5} \times 3 \sqrt{7} + 9 \sqrt{7} ^2\\ \\ 4 \times 5 + 2 \times 2 \sqrt{5} \times 3 \sqrt{7} + 9 \times 7 \\ \\ 20 + 2 \times 2 \sqrt{5} \times 3 \sqrt{7} + 9 \times 7 \\ \\ 20 + 2 \times 2 \times 3 \sqrt{5 \times 7} + 9 \times 7 \\ \\ 20 + 2 \times 2 \times 3 \sqrt{35} + 9 \times 7 \\ \\ 20 + 12 \sqrt{35} + 9 \times 7 \\ \\ 20 + 12 \sqrt{35} + 63 \\ \\ 83 + 12 \sqrt{35}$

The answer is: 83 + 12√35.

Answer 2

(2√(5) + 3√(7))²
(2√(5) + 3√(7))(2√(5) + 3√(7))
2√(5)(2√(5) + 3√(7)) + 3√(7)(2√(5) + 3√(7))
2√(5)(2√(5)) + 2√(5)(3√(7)) + 3√(7)(2√(5)) + 3√(7)(3√(7))
4√(25) + 6√(35) + 6√(35) + 9√(49)
4(5) + 12√(35) + 9(7)
20 + 12√(35) + 63
20 + 63 + 12√(35)
83 + 12√(35)