# Examine, Whether the Following Number Are Rational Or Irrational: Sqrt5-2 - Mathematics

Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads

Examine, whether the following number are rational or irrational:

sqrt5-2

Advertisement Remove all ads

#### Solution

Let x=sqrt5-2 be the rational number

Squaring on both sides, we get

x=sqrt5-2

x^2=(sqrt5-2)^2

x^2=5+4-4sqrt5

x^2=9-4sqrt5

(x^2-9)/(-4)=sqrt5

rArr(x^2-9)/(-4) is a rational number

rArrsqrt5 is a rational number

But we know that sqrt5 is an irrational number

So, we arrive at a contradiction

So (sqrt5-2) is an irrational number.

Concept: Concept of Irrational Numbers
Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 1 Number Systems
Exercise 1.4 | Q 3.09 | Page 31

#### Video TutorialsVIEW ALL [1]

Share
Notifications

View all notifications

Forgot password?