Question

Shaw that (√2+√3)² is an irrational number​

Answer 1

(√2+√3)^2

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

(√2)^2+(√3)^2 +2 x √2 x √3

2 + 3 + 2√6

5+2√6

root 6 is an irrational number so ,

5+√6 is an irrational number

Answer 2

If possible, let (√2+√3)^2 = p/q (a rational number)

then, (√2)^2 + (√3)^2 + 2√3.√2 =p/q

=> (√2)^2 + (√3)^2 + 2√3.√2 =p/q

=> 2 + 3 + 2√6 = p/q

=> 5 + 2√6 = p/q

=> 2√6 = p/q - 5

=>√6 = 1/2(p/q - 5)

As we know that,

Any irrational number is not equal to a rational number.

so what we've assumed is wrong so (√2+√3)^2 is an irrational number.

Hope it helps...

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