Q16 of 23 Page 1

Prove that is anirrational number.


Let be a rational number, say r
Then
On squaring both sides,

using (a  +  b) 2 =a 2 +  2ab  +  b 2

Now is a rational number and is an irrational number.
Since a rational number cannot be equal to an irrational number. Our assumption that is rational is wrong.

More from this chapter

All 23 →
14

Find the value of √5correct to two places of decimal.

15

Prove that √ 3-√2 is irrational.

17

Examine, whether the following numbers are rational or irrational:
(i)
(ii)
(iii)
(iv)

18

Prove that
(a) is not arational number and
(b) is not arational number.