Question

ab = 6 which is rational.
EXERCISE - 1.4
Prove that the following are irrational
1
(i)
on
√2
(i) 13 + 5
onal​

Answer 1

(i) Let us assum to the contrary that √2 is rational,

Such that,

√2 = a/b (b is not equal to 0)

where a and b are co-prime,

Squaring both sides, we get

(√2)² = (a/b)²

2 = a²/b²

2b² = a²

b² = a²/2. .... (eq.1)

• a² is divisible by 2

So, a is also divisible by 2

Let a = 2c ( where c is some integer)

From eq.1

b² = a²/2

b² = (2c)²/2

b² = 4c²/2

b² = 2c²

c² = b²/2

• b² is divisible by 2

So, b is also divisible by 2

• From above statements it is clear that a and b have 2 as their common factor which contradicts our fact that a and b are co-prime

• Therefore, our assumption that √2 is rational is wrong.

Hence,

° √2 is irrational.