Question

prove that 5- root3is irrational​

Answer 1

Answer:

I t is the irrational number

Answer 2

Answer:

Let 5✓3 be a rational no.

So it can be written in form of p/q (p and q are conjugate no.)

5✓3=p/q

q5✓3=p

Squaring both sides-

(q)^2. 75=(p)^2 { (5)^2=25,(✓3)^2=3, 25×3=75 }

(q)^2=(p)^2/75

Here, (p)^2 is divisible by 75

It means, p is also divisible by 75 ...(1)

Now taking p as r

(q)^2=(r)^2. 75

(q)^2/75=(r)^2

Here, (q)^2 is divisible by 75

It means q is also divisible by 75...(2)

But p and q are conjugate no.

So, it is not possible.

Means our supposition is wrong.

Hence, 5✓3 is irrational.