# Examine, Whether the Following Number Are Rational Or Irrational: (Sqrt2+Sqrt3)^2 - Mathematics

Examine, whether the following number are rational or irrational:

(sqrt2+sqrt3)^2

#### Solution

Let x=(sqrt2+sqrt3)^2be rational number

Using the formula (a + b)2 = a2 + b2 + 2ab

rArrx=(sqrt2)^2+(sqrt3)^2+2(sqrt2)(sqrt3)

rArrx=2+3+2sqrt6

rArrx=5+2sqrt6

rArr(x-5)/2=sqrt6

rArr(x-5)/2 is a rational number

rArrsqrt6 is a rational number

But we know that sqrt6 is an irrational number

So, we arrive at a contradiction

So (sqrt2+sqrt3)^2 is an irrational number.

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 3.08 | Page 31