Question

Show
that
5root3
is
irrational​

Answer 1

Answer:

HEYA MATE HERE IS UR 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

Answer:

Hence Proved

Step-by-step explanation:

Let 5√3 be rational number

5√3 = p/q , pand q are coprimes, q≠0

√3 = p/5q

Here √3 is irrational therefore p/5q should be irrational but it is rational number as p and q are coprimes

Therefore it contradicts our assumption that 5√3 is rational

Hence 5√3 is an irrational number

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