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

Question

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## Answers ( )

Answer:irrational number

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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