Question

The area of square is 12+2 under root 35 then find its side

Answer 1

Area of square is =
${side}^{2}$
$12 + 2 \sqrt{35} = {a}^{2} \\ \\ {a}^{2} - 12 = 2 \sqrt{35} \\ \\ {( {a}^{2} - 12)}^{2} = 4 \times 35 \\ \\ {a}^{4} + 144 - 24 {a}^{2} = 140 \\ \\ {a}^{4} - 24 {a}^{2} + 144 - 140 = 0 \\ \\ {a}^{4} - 24 {a}^{2} + 4 = 0 \\ \\ {a}^{2} = \frac{24 + - \sqrt{24 \times 24 - 16} }{2} \\ \\ {a}^{2} = \frac{24 + - 23.67}{2} \\ \\ {a}^{2} = 47.67 \div 2 \: \: \: \: = 23.83 or\\ \\ a = \sqrt{23.83}$