Question

Prove that 5 - V3 is irrational, given that v3 is irrational.
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Answer 1

Answer:

Let us assume the given number be rational and we will write the given number in p/q form

⇒5−

3

=

q

p

⇒

3

=

q

5q−p

We observe that LHS is irrational and RHS is rational, which is not possible.

This is contradiction.

Hence our assumption that given number is rational is false

⇒5−

3

is irrational

Answer 2

Step-by-step explanation:

Here is your answer

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.