Rationalisation is a process that finds application in elementary algebra, where it is used to
eliminate the irrational number in the denominator of a fraction. That is, remove the
radicals in a fraction so that the denominator only contains a rational number. There are
many rationalising techniques which are used to rationalize the denominator. The word
rationalize literally means making something more efficient. Usually, having a radical
(root) in numerator is okay, but having a radical (root) in the denominator is not. This is
because just to avoid tedious computations. It is cumbersome to divide a number by an
irrational number. Let us look at a situation with irrational numbers in the denominator.
A peasant wants to plough his rectangular field of dimensions
√
deca metres and
√
deca metres. Also, he wants to fence all around his field. For this he has to spend
money at the rate of ` 25/m2
for ploughing and ` 10/m for fencing.
i. What is the area of the rectangular field?
a. 1 m2 b. 100 m
2
c. 1 hectare d. 1 decameter
ii. What is the total cost of the fencing of the rectangular field?
a. ` 280 b. ` 28 c. ` 2800 d. ` 0.28
iii. How much money did the peasant spent for ploughing the rectangular filed?
a. ` 255 b. ` 250 c. ` 2550 d. ` 2500
iv. If √ = 1.414, then the value of
√
is
a. – 2.414 b. 2.414 c. – 2.141 d. 2.141
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