Question

Prove that
2 + √3
is an irrational number, given that √3 is an irrational number.

Answer 1

Step-by-step explanation:

Given:-

√3 is an irrational number.

To Prove:-

Prove that 2 + √3 is an irrational number

Proof:-

Given number=2+√3

Let us assume that

2+√3 is a rational number

It must be in the form of p/q

2+√3=a/b(a,b are co - primes)

=>√3=(a/b)-2

=>√3=(a-2b)/b

from above equation

√3 is in the form of p/q

so √3 is a rational number

but given that √3 is an irrational number

so our assumption is wrong

So 2+√3 is not a rational number

It is an irrational number.

Hence, Proved

Using method:-

Indirect method(Method of Contradiction)