Question

if √5 is an irrational,then prove that 3+√5 is an irrational​

Answer 1

the answer is on the photo

please equate your value on my steps

Answer 2

Answer:

$\huge\colorbox{yellow}{Solution\:-}$

3 + √5

Let 3+√5 be rational

So, 3+√5 = a\b. ( where a and b are integers)

=> √5 = a - 3b/ b

a - 3b/ b is rational and √5 is irrational

LHS ≠ RHS

Our aussumption is wrong

Therefore, 3 + √5 is irrational