Question

prove that 2 minus root 5 is an irrational number​

Answer 1

hey dude !!!

=>> 2-√5 be a rational number

2-√5 = p/q (where p&q is a coprime intgers and q is not equal to 0 )

-√5 = p/2q

[√5 = -p/2q ]------------(1)

-p/2q = rational number. ( bcoz p & q are co prime ) --------------(2)

from (1)&(2)

√5 = rational number

which is not possible...

therefore our supposition of assuming 2-√5 was wrong ...

therefore it's irrational number

HENCE PROVED

hope this helps you ^_^

Answer 2

Step-by-step explanation:

Let 2-√5 is rational number so

2-√5 = p/q

Where q≠0 and p and q is coprime and we also known that 2 is rational no.

Now

√5 =-(p/q-2)

√5 = 2-p/q

Taking l.c.m we get

√5 = 2q-p/q

As we know that root 5is irrational no and how a irrational no.can be equal to a rational no. So here is a contraction.Hence

2-√5 is a irrational no.