# Examine, Whether the Following Number Are Rational Or Irrational: Sqrt3+Sqrt5 - Mathematics

Examine, whether the following number are rational or irrational:

sqrt3+sqrt5

#### Solution

Let x=sqrt3+sqrt5 be the rational number

Squaring on both sides, we get

rArrx^2=(sqrt3+sqrt5)^2

rArrx^2=3+5+2sqrt15

rArrx^2=8+2sqrt15

rArrx^2-8=2sqrt15

rArr(x^2-8)/2=sqrt15

Now, x is rational number

⇒ x2 is rational number

⇒ x2 - 8 is rational number

rArr (x^2 -8)/2 is rational number

rArrsqrt15 is rational number

But sqrt15 is an irrational number

So, we arrive at a contradiction

Hence sqrt3+sqrt5 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 3.05 | Page 31