Question

Prove that 5 + √3 is irrational.​

Answer 1

Step-by-step explanation:

$5 + \sqrt{3 } \\ 5 + \sqrt{3} \times \frac{5 + \sqrt{3} }{5 - \sqrt{3} } \\ \frac{25 + 3 + 10 \sqrt{3} }{5 - \sqrt{3} } \\ \frac{28 + 10 \sqrt{3} }{5 - \sqrt{3} }$

so ,multiply by conjugate but squreroot is remaining so this number irrational

Answer 2

Answer:

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

⇒5- √3= p/q

⇒√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− √3 is irrational

Step-by-step explanation:

Hope it will help you..