Math, asked by wwwnaninani33, 6 months ago

prove that 5-3√2 is an irrational​

Answers

Answered by hritik76
1

Answer:

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Answered by singhkarishma882
3

\huge\red {\boxed {\mathfrak {☆AnSwEr☆}}}

Let, us assume that 5-3\sqrt {2} is a rational number.

Such that, 5-3\sqrt {2}\:=\:\frac {p}{q}where p and q are co-primes.

Rearranging the equation, we get :-

3 \sqrt{2}  =  \frac{p  -  5}{q}

 \sqrt{2}  =  \frac{p - 5q}{q}

Since, p and q are co-primes, we get \frac {p-5q}{q} is rational number and \sqrt {3} is rational number.

But,

this contradicts the fact that \sqrt {3} is irrational

This Contradiction has arisen because of our incorrect assumption that 5-\sqrt {3} is rational.

So, we conclude that5-\sqrt {3} is irrational.

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