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

Question

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

in progress 0
Ariana 1 month 2021-08-20T05:54:20+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-08-20T05:56:05+00:00

    Answer:

    irrational number

    I hope this is helpful to you!

    0
    2021-08-20T05:56:15+00:00

    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

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