Question

4.
5. Prove that (2 + 3) is an irrational number, given that 3 is an irrational
number.
[CBSE 2018
loma​

Answer 1

$\huge\bold\green{Correct Question:-}$

Prove that 2+√3 is an irrational number.

$\huge\bold\green{Answer:-:}$

Let us assume that :-

2 + √3 is a rational number.

Let , 2 + √3   = r , where "r" is a rational number

Squaring both sides ,

[2 + √3 ]² = r²

2² + 2 x 2 x √3 + [√3]²  = r²

4 + 4√3 + 3 = r²

7 + 4√3 = r²

4√3 = r² - 7

√3 = r² - 7÷ 4

So , 

we see that LHS is purely irrational.

But , on the other side , RHS is rational.

This contradicts the fact that 2+√3 is rational.

Hence , our assumption was wrong.

Hence ,

2+√3 is a irrational number.

Answer 2

Step-by-step explanation:

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