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Prove that Following Numbers Are Irrationals: 5 √ 2 - Mathematics

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प्रश्न

Prove that following numbers are irrationals:

\[5\sqrt{2}\]
संख्यात्मक

उत्तर

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

\[5\sqrt{2}\]`=a/b`

`sqrt2=a/b-5`

`sqrt5=(a-5b)/b`

`sqrt2` is a rational which is a contradication

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अध्याय 1: Real Numbers - Exercise 1.5 [पृष्ठ ४९]

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आरडी शर्मा Mathematics [English] Class 10
अध्याय 1 Real Numbers
Exercise 1.5 | Q 2.4 | पृष्ठ ४९

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