Question

prove 2 minus root 5(2-√5)
step by step
so we have to take out root of every root number
​

Answer 1

If possible, let us assume 2+ 5

is a rational number.

2+ 5=qp

where p,q∈z,q



=0

2−qp=-5

q

2q−p

=−

5

⇒− 5

is a rational number

∵

q

2q−p

is a rational number

But −5 is not a rational number.

∴ Our supposition 2+ 5

is a rational number is wrong.

⇒2+ 5

is an irrational number.

hope it helps you