# Examine, Whether the Following Number Are Rational Or Irrational: (Sqrt2-2)^2 - Mathematics

Examine, whether the following number are rational or irrational:

(sqrt2-2)^2

#### Solution

Let x=(sqrt2-2)^2 be a rational number.

x=(sqrt2-2)^2

rArrx=2+4-4sqrt2

rArrx=6-4sqrt2

rArr(x-6)/(-4)=sqrt2

Since, x is rational number,

⇒ x – 6 is a rational nu8mber

rArr(x-6)/(-4) is a rational number

⇒ sqrt2is a rational number

But we know that sqrt2 is an irrational number, which is a contradiction

So (sqrt2-2)^2 is an irrational number

Concept: Concept of Irrational Numbers
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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 1 Number Systems
Exercise 1.4 | Q 3.06 | Page 31

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