Question

3. Prove that (5+V3) is an irrational number.​

Answer 1

Step-by-step explanation:

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

let us assum that 5-√3 is rational number so we can find two integers a , b. ... So it arise contradiction due to our wrong assumption that 5 - √3 is rational number. Hence, 5 -√3 is irrational number.

2)

Hey mate here is your answer

=> 5 - √3

Solution:

let us assum that 5-√3 is rational number so we can find two integers a , b. Where a and b are two co - primes number.

= 5-√3 = a/b

= √3= 5- a/b

=> a and b are integers so (5 - a/b ) is rational

But √3 is irrational ( we know that and it is given)

So it arise contradiction due to our wrong assumption that 5 - √3 is rational number.

Hence, 5 -√3 is irrational number.