Q12 of 44 Page 1

Prove that 4 - √3 is irrational. (CBSE 2008)

Let x = 4 - √3 and let us assume that x is rational.


For x to be rational, .


So,





Now, x is rational, will also be rational. But √3 is irrational. So, the statement made is wrong. Hence, 4 - √3 is irrational.


More from this chapter

All 44 →
10

Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9m, 9m + 1 or 9m + 8. (CBSE 2009)

 11

Show that one and only one out of n, (n + 2) and (n + 4) is divisible by 3, where n is any positive integer. (CBSE 2008)

 13

Show that is an irrational number. (CBSE 2008)

 14

Prove that 2 - 3√5 is an irrational number. (CBSE 2010)