Worked Solution to Homework 3(a), Homework 3(b) & Homework 3(c)

Click at the following links to view full set of worked solution

It is your responsibility to go through the marked copies returned to you, to check against the working and answers expected; and do corrections when applicable.

What do you need to do:

  • Do corrections when applicable, in particular the presentation of your working.
  • Make appointment to see Ms Loh during the TS/C period for consultation to clarify your doubts.

Homework 3(a)
In Q3(b), we discussed and noted that the square root of a number can give rise to 2 possible values. Illustrating with the example:
  • When we square a positive number 6, 6 x 6 = 36
  • Square root of 36 will give us 6 (since square & square root are 'reverse' operations)
  • When we square a negative number (-6), (-6) x (-6) = 36
  • Hence, the square root of 36 could also give rise to (-6).
Hence, in general, when NO specific conditions is given, we should have two answers for the square root of a number. In this example, Square of 36 = 6 or -6

In Q8, we learnt that, by looking at the divisibility of the power to the number, we are able to tell if we can square root or cube root the number.
This is also one reason why we tend express numbers in Index notation when operating on the roots of the number.

Homework 3(b)
In Q18, note that there are 2 parts to the question.
Part (b) specifically mention "Hence, find...", which means we are expected to use of what was obtained in Part (a) to work on the next part.
  • Do not use other methods such as Guess and Check.
  • Check out the proper way of presenting the working for Q18(b)

Homework 3(c)
When given questions similar to Q19(b), do not attempt to evaluate the value using the calculator. Most of the time, it makes reference to the previous part where you are required to express the number in prime factorisation form.

Always check if any number 'housed' under the root sign is already expressed in the prime factorsiation form. If not, factorise them before simplifying the terms under the root sign.

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