Math, asked by rajdeep17, 1 year ago

show that 3√3 is an irrational

Answers

Answered by Róunak
7
Hey mate..
========

Let us assume to the contrary that
3 \sqrt{3}
is a rational number.

So,

3 \sqrt{3} = \frac{p}{q} ( where p,q are co-prime numbers and q is not equal to zero )

 = > \sqrt{3} = \frac{p}{3q}

Since, p and q are integers,  \frac{p}{3q} is a rational number .

So,
 \sqrt{3} is a rational number

But it is impossible since,
3 \sqrt{3}
is irrational .

So, We came to conclusion that , 3 \sqrt{3} is an irrational number.

( Hence, Proved )

Hope it helps !!

rajdeep17: awesome thank you
Róunak: no problem
rajdeep17: i have one more question
Róunak: ok
Róunak: post
Similar questions