Question

Page No.:
The number (2+√3)
is
1) a whole number
2) an integer
3) a rational number
4) an irrational number​

Answer 1

Answer:

irrational number

I hope this is helpful to you!

Answer 2

Answer:

a irrational number

proof We can prove it by contradictory method..

We assume that 2 + √3 is a rational number.

=> 2 + √3 = p/q , where p & q are integers, ‘q’ not = 0.

=> √3 = (p/q) - 2

=> √3 = (p - 2q)/ q ………… (1)

=> here, LHS √3 is an irrational number.

But RHS is a rational number.. Reason- the difference of 2 integers is always an integer. So the numerator (p- 2q) is an integer.

& the denominator ‘q’ is an integer.&‘q’ not = 0

This way, all conditions of a rational number are satisfied.

=> RHS (p- 2q)/q is a rational number.

But , LHS is an irrational.

so sum will be irrational