Prove that the Following is Irrational 1 √ 2 - Mathematics

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Prove that the following is irrational


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`1/sqrt2 xx sqrt2/sqrt2 = sqrt2/2`

Let a = `(1/2)sqrt2` be a rational number

⇒ 2a = `sqrt2`

2a is a rational number since product of two rational number is a rational number.

Which will imply that `sqrt2` is a rational number. But it is a contradiciton since `sqrt2` is an irrational number.

Therefore 2a is irrational or a is irrational

Therefore `1/sqrt2` is irrational. Hence proved

Concept: Concept of Irrational Numbers
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Chapter 1: Real Numbers - Exercise 1.3 [Page 14]


NCERT Class 10 Maths
Chapter 1 Real Numbers
Exercise 1.3 | Q 3.1 | Page 14

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