Question

Prove that:
a) 5+root 6 divided by 2
is irrational

Assume
that 5+ root 6
is rational. So

it
can be

in expressed
the form
P by Q where Р
and q are coprimes,
q is not equal to zero

​

Answer 1

Answer:

Let us assume that √5 is a rational number.

we know that the rational numbers are in the form of p/q form where p,q are coprime numbers.

so,

5

=

q

p

p=

(

5)q

we know that 'p' is a rational number. so

(

5)q must be rational since it equals to p

but it doesnt occurs with

(

5)q since its not an integer

therefore, p is not equal to

(

5)q

this contradicts the fact that

(

5) is an irrational number

hence our assumption is wrong and

(

5) is an irrational number

How satisfied are you with the answer?

Step-by-step explanation:

Let us assume that √5 is a rational number.

we know that the rational numbers are in the form of p/q form where p,q are coprime numbers.

so,

5

=

q

p

p=

(

5)q

we know that 'p' is a rational number. so

(

5)q must be rational since it equals to p

but it doesnt occurs with

(

5)q since its not an integer

therefore, p is not equal to

(

5)q

this contradicts the fact that

(

5) is an irrational number

hence our assumption is wrong and

(

5) is an irrational number

How satisfied are you with the answer?