Page 115 - Mathematics_Form_Two

Exponents and radicals

16. A rectangular plot of land has an area of 5000 square metres. If the length of the
plot is metres, what is the width of the plot?

17. A box has a volume of 54000 cubic centimetres. If the height of the box is
300 centimetres, what is the area of the base?
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18. The height of a tree is 320 metres. Another tree has a height of 180 metres.
What is the ratio of the heights of the two trees?

19. A cylindrical tank has a volume of 288 cubic metres. If the height of the tank
is 18 metres, what is the area of the base of the cylinder? Mathematics for Secondary Schools

Rationalisation of denominators

Rationalisation of a denominator involves eliminating radicals from the denominator
of a fraction. This makes denominator, to be a rational number. The procedure for
rationalising the denominator are as follows:
(i) If the denominator is a single radical term, multiply the numerator and the
denominator by the radical in the denominator.

For example, in rationalising the denominator of a , multiplying both the
b
numerator and denominator by b as follow.

a = a ´ b = ab
b b b b

Therefore, a = ab .
b b

(ii) If the denominator is a sum or difference of two radicals, change the sign
connecting the two terms. The resulting expression is called the rationalising
factor, which is then multiplied in the numerator and the denominator.

1
For example, in rationalizing the denominator of . , the rationalising
a + b
factor is a . b -

Multiply both the numerator and the denominator by a b - as follows.

1 = 1 ´ a b - = a b -
-
a b + a b + a b - ab

1 a − b
Therefore, . = .
−
a + b ab

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Student's Book Form Two

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