Question

prove that 5√2 is irrational​

Answer 1

Step-by-step explanation:

Answer

We have to prove

2

is irrational.

Let us assume

2

is rational

2

=

b

a

( a and b has no common factions but 1 )

⇒2=

b

2

a

2

2b

2

=a

2

( hence a is even )

let a=2k

⇒2b

2

=(2k)

2

⇒b

2

=2k

2

( Hence b is even as well )

This contradicts as both a and b are even, ( 2 as common factor )

Hence,

2

is irrational.

Hence, proved.

Answer 2

Answer:

We have to prove

2

is irrational.

Let us assume

2

is rational

2

=

b

a

( a and b has no common factions but 1 )

⇒ 2=

b 2

a 2

2b

2

=

a 2

( hence a is even )

let

a=

2k

⇒ 2b

2

=

(2k) 2

⇒

b 2

2k

2

This contradicts as both a and b are even, ( 2 as common factor )

Hence,

2

is irrational.

Hence, proved.