Examine, Whether the Following Number Are Rational Or Irrational: `Sqrt3+Sqrt2` - Mathematics

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Examine, whether the following number are rational or irrational:


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Let `x=sqrt3+sqrt2` be the rational number

Squaring on both sides, we get






Since, x is rational number

⇒ x2 is rational

⇒ x2 - 5 is rational

`rArr(x^2-5)/2` is rational number

`rArr sqrt6` is rational number

But, `sqrt6` is an irrational number

So, we arrive at contradiction

Hence, `sqrt3+sqrt2` is an irrational number.

Concept: Concept of Irrational Numbers
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RD Sharma Mathematics for Class 9
Chapter 1 Number Systems
Exercise 1.4 | Q 3.04 | Page 31

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