Question

prove 3+2root5 irrational

Answer 1

Hey... I think this can be ur answer!!

Let u assume that 3+2root5 is rational.
So,
3+2root5 = a/b (a and b are Co prime)

Now,
2root5 = a/b-3 = a-3b/b
Root5 = a - 3b/2b
But we know that root5 is irrational
Hence our assumption was wrong...

SO, 3+2root5 is irrational..

Hence proved

Hope it helps you dear ☺️☺️
Have a great time!!

Answer 2

3+2root5
we know that any prime number's root is irrational numbers
and 5 is a prime number
so the root of 5 is a irrational number
and when we multiple any rational number with any irrational number
the product is irrational number
and 2 is rational number and root 5 is a irrational number
so,2×root5
=2root5 is a irrational number
when we add any irrational number with rational number
the value is irrational number
and 3 is a rational number
2root5 is a irrational number
3+2root5 is a irrational number
hence proved 3+2root5 is a irrational number
Hope it helps you