# Prove that 3 + 2sqrt5 is irrational - Mathematics

Prove that 3 + 2sqrt5 is irrational

#### Solution

if possible let a = 3 + 2sqrt5 be a rational number.

Squaring a2 = (3+2sqrt5)2

a2 = 29 +12sqrt5

sqrt5 = (a^2 - 29)/12 ........(1)

Since a is a rational number the expression (a^2-29)/12 is also rational number.

⇒ sqrt5 is a rational number.

This is a contradiction. Hence, 3 + 2sqrt5 is irrational.

Hence Proved.

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

NCERT Class 10 Maths
Chapter 1 Real Numbers
Exercise 1.3 | Q 2 | Page 14