# Prove that the Following is Irrational 1 √ 2 - Mathematics

Sum

Prove that the following is irrational

1/sqrt2

#### Solution

1/sqrt2

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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#### APPEARS IN

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