Question

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

Answer 1

Heya!!
Here is your answer:&
We have to check whether (√2+2)^2 is a rational number or a irrational number.
First we will expand this number using the identity:-
(a+b)^2=a^2+b^2+2.a.b
Here the dot represents the sign of multiplication.

(√2+2)^2
Here a= √2 and b=2
(√2)^2+(2)^2+2.√2.2
2+4+4√2
6+4√2( This is the expanded form)
We know that √2 is an irrational number .
That's why 4√2 is an irrational number.
And therefore 6+4√2 is an irrational number .

Hence, (√2+2)^2 is an irrational number.

Hope it helps you.