Question

show that 5 minus root 3 is irrational

Answer 1

Let us assume that 5 - root 3 is rational. Then it can be written in the form

5 - root3 = p/q

or 5 - p/q = root3

It implies root3 is a rational number [Since 5 - p/q are rationals]

But this contradicts to the fact that root 3 is irrational. Hence our supposition was wrong. Therefore 5 - root 3 is irrational.

Answer 2

Answer:

Step-by-step explanation:

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

⇒5−root 3=p/q

⇒ root 3= 5q-p/q

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- root 3 is irrational

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