Let 3+2√5= p/q is rational number
√5=(p-3q)/2qRHS is rational but LHS √5 is not a rational number So 3+2√5 is an irrational numberHENCE PROVED
bro first prove root two is irrational then anything multiplied with irration is irrational
Let us assume that 3+2√5 is a rational number.
3+2√5 = a/b [a,b are co-primes ; where b is not equal to 0]
2√5 = a/b-3
2√5 = a-3b/b
√5 = a-3b/2b
An irrational is never equal to a rational . This is a contradiction. Our assumption must be wrong .
Therefore, 3+2√5 is an irrational number.
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Let us suppose that √3 + √5 is rational. Let √3 + √5 = a, where a is rational.
write image in between that given above
As the right hand side is rational number while V5 is irrational. Since, 3 and 5 are prime numbers. Hence, √3 + √5 is irrational.
under root =/ okkk
so /3+/5=p divided by Q (Q=not to 0) and p and q are coprime
so first /3
sqare both side
so as based on this p is a factor of 3a
by solving we get that 3 is also a factor of Q
so p and Q are mot coprime
so /3 is irrational
so lly /5 is also irrational so /3+/5 is also orrqtional
21. prove that 3+2v5 is an irrational number....