Question

solve this question


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༎༎༎༎༎༎༎༎༎༎༎༎༎
༎༎༎༎༎༎༎༎
༎༎༎༎།
༎།།
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Answer 1

it's irrational because when we open square a root value will also come let's try it
= (√2+2)^2
= (√2)^2 + (2)^2 + 2×√2×2
= 2 +4+4√2
6+4√2
let 6+4√2 is rational no.
6+4√2 =p/q ( rational no)
4√2=p/q -6
4√2 = p -6q/q
√2 =p-6q/4q
here LHS is irrational
RHS is rational
hence LHS is not equal to RHS
ur supposition is wrong
(√2+2)^2 is irrational no .
now next ans
if a+ b is even
when even value substract each other and Will also come in even.
let take a example
4+2=6
4-2=2
hence proved.

Answer 2

1. fist ques your
2. $( \sqrt{2} + 2 {)}^{2}$
3. it's irrational number because.

like this

$\sqrt{2}^{2} + 2 \times \sqrt{2} \times 2 + {2}^{2} \\ \sqrt{4} + 4 \sqrt{2} + 4 \\ \\ \\ that \: is \: reason \: why \: your \: ans \: not \: come \: in \: rational \:$

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second ans is (a+b)=is a natural number... because a and b also natural number...

and (a-b)

is also natural number...

because this (a-b) multiple both ans come same but only difference in plus and minus...

So you second ans is...

That is your natural number....

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