Question

prove that 3+2√5 is an irrational number​

Answer 1

REFER TO THE ATTACHMENTS❤️❤️

Answer 2

Let 2√5 is a rational number.

2√5 = p/q

Squaring on both side we get, then we get

4(5) = p^2/q^2

20 = p^2/q^2

20q^2 = p^2

p^2 is a multiple of 20

Therefore, p is also a multiple of 20

Therefore, P has a factor of 20

P^2/20 = q^2

q^2 is also a multiple of 20

Therefore, q is also a multiple of 20

Therfore, q also has a factor of 20.

Hence, both p and q has a factor of 20 except 1.Hence our consideration is wrong.

Therefore 2√5 is an irrational number.

As we know that if any natural number is added with irrational number than it must be irrational.

Hence prove 3+2√5 is an irrational number.