Question

examine whether the following numbers are rational or irrational (√2+1/√2)^2​

Answer 1

= (√2 + 1/√2)^2

Using Identity (a+b)^2 = a^2 + 2ab + b^2

= (√2)^2 + 2×√2×1/√2 + (1/√2)^2

= 2 + 2 + 1/2

= (4+4+1)/2

= 9/2

Answer 2

(a+b)²=a²+b²+2ab

${ (\sqrt{2} + \frac{1}{ \sqrt{2} } )}^{2} = ( { \sqrt{2} })^{2} + ( { \frac{1}{ \sqrt{2} } })^{2} + 2 \times \sqrt{2} \times \frac{1}{ \sqrt{2} } \\ 2 + \frac{1}{2} + 2 \\ \frac{4 + 1 + 4}{2} = \frac{9}{2}$