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Prove that Following Numbers Are Irrationals: 4 + √ 2 - Mathematics

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प्रश्न

Prove that following numbers are irrationals:

\[4 + \sqrt{2}\]
संख्यात्मक

उत्तर

Let us assume that `4+sqrt2` is rational .Then , there exist positive co primes a and bsuch that

`4+sqrt2=a/b`

`sqrt2=a/b-4`

`sqrt=(a-4b)/b`

`sqrt2` is a rational numbers which is a contradication.
Hence \[4 + \sqrt{2}\] is irrational
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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 2.3 | पृष्ठ ४९

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