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Prove that 2 − 3 √ 5 is an Irrational Number. - Mathematics

Numerical

Prove that \[2 - 3\sqrt{5}\] is an irrational number.

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Solution

Let us assume that \[2 - 3\sqrt{5}\] is rational .Then, there exist positive co primes a and b such that

`2-3sqrt5=a/b`

`3sqrt5=a/b-2`

`3sqrt5=(a/b-2)/3`

`sqrt5=(a-2b)/(3b)`

This contradicts the fact sqrt5 is an irrational number 

Hence `2-3sqrt5` is irrational 

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Class 10 Maths
Chapter 1 Real Numbers
Exercise 1.5 | Q 8 | Page 49
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