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

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प्रश्न

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

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उत्तर

Let us assume that `5-2sqrt3` is rational .Then, there exist positive co primes a and b such that

\[5 - 2\sqrt{3}\] `=a/b`
`2sqrt3=a/b-5`
`sqrt3=((a/b)-5)/2`
`sqrt3= (a-5b)/(2b)`
This contradicts the fact that `sqrt3` is an irrational 
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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1: Real Numbers - Exercise 1.5 [पृष्ठ ४९]

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आरडी शर्मा Mathematics [English] Class 10
पाठ 1 Real Numbers
Exercise 1.5 | Q 6 | पृष्ठ ४९

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