Question

We proov that √3 is irrational hense proov that 7+2√3 is also irrational

Answer 1

Answer:

Let root 3 be rational of the form p\q where p and q are co primes

root3 =p\q     squaring on both side

3=p*2\q*2

3q*2=p*2-----------1

here p*2 is divided by 3 so as p divides 3

p=3a

p*2=9a*2 substituting in 1

3q*2=9a*2

q*2=3a*2

here even 3 divides q*2 and q

p and q has common factor 3

but this contradicts the fact that they are co prime

so our assumption is wrong

root 3 is irrational

let 7+2root3 be rational

7+2root 3=p\q

2 root3=p-7q\q

root3=p-7q\2q

this shows root 3 is rational but we know that it is irrational so 7+2root3 is irrational

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Answer 2

Let 7+2√3 be a rational number.

Then,7+2√3=a/b,where a and b are Coprime integers and b is not= 0.

Therefore,2√3=a/b-7

√3=a/2b-7

Here,a/2b-7 is a rational number.

We know that,√3 is an irrational number.

Hence,our assumption is incorrect.

Therefore,7+2√3 is an irrational number.

Hence proved

Hope it helps ........

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