Question

show that 5+2) is not a rational number​

Answer 1

Answer:

To prove 5+

2

is irrational,

Let us assume

2

is rational

⇒

2

=

b

a

(a and b has no common factors except 1 )

⇒ 2=

b

2

a

2

⇒ 2b

2

=a

2

Hence a is even ...(1)

Let a=2k

⇒2b

2

=(2k)

2

⇒b

2

=2k

2

Hence b is also even ...(2)

This contradicts our assumptions as both a and b are even because they have 2 as the common factor.

Hence,

2

is irrational.

Hence, proved.

Answer 2

Answer:

a rational number is only written in the form of p/q

therefore 5+2) is not a rational number