Question

prove that 5 - root 3 is irrational

Answer 1

Hey dear here is your answer ^_^

⭐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.

CHEERZ!

Hope it helped you out ⭐^_^⭐
Thanks ⭐(^^)⭐

Answer 2

Step-by-step explanation:

As per the data given in the question,

To prove: 5-√3 is irrational

Assumption: Let 5-√3 be rational.

which means 5-√3 can be expressed in form of p/q

so,

$5-\sqrt{3} =\frac{p}{q}\\5-\frac{p}{q}=\sqrt{3}$

Since 5 is rational and p/q is rational, so it means that 5 - p/q is rational

And through the eqation it says that √3 is also rational, which is false

so, our assumption goes wrong here.

Hence, 5-√3 is irrational

#SPJ2