Question

examine whether (√3+3)^2 is rational or irrational​

Answer 1

[√3+2]^2

[(√3)^2+2*√3*2+2^2]

[3+4√3+4]

7+4√3

it is an irrational.

 

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Answer 2

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Using Identity

➡ ( a + b )^2 = a^2 + b^2 + 2ab

➡ ( √3 + 3 )^2 = √3^2 + 3^2 + 2(√3)(3)

= 3 + 9 + 6√3

= 12 + 6√3 ( Irrational )