Question

prove that 7+√5 is irrational, given that √5 is irrational​

Answer 1

Answer:

Let us assume to the contrary that 7

5

is rational number

i.e, we can find co-prime a & b where b



=0 such that:-

⇒7−

5

=

b

a

⇒7−

b

a

=

5

by rearranging this equation we get

⇒

5

=7−

b

a

⇒

5

b=7b−a

since a & b are integers,we get

b

7b−a

is a rational number & so

5

is rational But, this contradicts the fact that

5

is irrational number.

∴ our assumption i.e, 7−

5

is rational number is incorrect.

Hence, 7−

5

is irrrational

hope this helps you