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Question

Match the following to their simplified values.

A
2+3
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B
4
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C
11 + 62
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Solution

Using the identity, (a+b)(a-b) = a2-b2,
(35)×(3+5)
=32(5)2
= 95
= 4

In order to rationalise 123,
we multiply the numerator and denominator by (2+3) .

123=123×2+32+3

=2+32232=2+31=2+3.

Using the identity,
(a+b)2 = a2+ 2ab + b2,

(3+2)2=32+22+2(3)2
=9+2+62
=11+62.

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