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JSS2: MATHEMATICS - 1ST TERM

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  1. Properties of Whole Numbers I | Week 1
    4 Topics
    |
    1 Quiz
  2. Properties of Whole Numbers II | Week 2
    4 Topics
    |
    1 Quiz
  3. Properties of Whole Numbers III | Week 3
    5 Topics
    |
    1 Quiz
  4. Indices | Week 4
    2 Topics
    |
    1 Quiz
  5. Laws of Indices | Week 5
    5 Topics
    |
    1 Quiz
  6. Whole Numbers & Decimal Numbers | Week 6
    4 Topics
    |
    1 Quiz
  7. Standard Form | Week 7
    3 Topics
    |
    1 Quiz
  8. Significant Figures (S.F) | Week 8
    4 Topics
    |
    1 Quiz
  9. Fractions, Ratios, Proportions & Percentages I | Week 9
    6 Topics
    |
    1 Quiz
  10. Fractions, Ratios, Proportions & Percentages II | Week 10
    4 Topics
    |
    1 Quiz
  11. Fractions, Ratios, Proportions & Percentages III | Week 11
    3 Topics
    |
    1 Quiz
  12. Approximation & Estimation | Week 12
    1 Topic
    |
    1 Quiz
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Topic Content:

  • Perfect Square

A perfect square is a whole number whose square root is a whole number.  Examples

9 = 3 × 3…………… \(\scriptsize \sqrt{9}\) = 3
4 = 2 × 2…………… \(\scriptsize \sqrt{4}\) = 2
1 = 1 × 1…………… \(\scriptsize \sqrt{1}\) = 1
16 = 4 × 4…………… \(\scriptsize \sqrt{16}\)= 4
25 = 5 × 5…………… \(\scriptsize \sqrt{25}\) = 5
36 = 6 × 6…………… \(\scriptsize \sqrt{36}\)= 6

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196 etc are perfect squares because their square roots are whole numbers.

Worked Example 2.3.1:

Find the smallest number by which 27 must be multiplied to make it a perfect square.

Solution

Step 1:  Express 27 as a product of its prime factors.

Screenshot 2023 08 20 at 04.41.33

Step 2: Pick the product of prime factors in pairs of the same digits. Then multiply digits without pairs (stand-alone digits) together. This gives the required number. i.e.

Screenshot 2023 08 20 at 04.43.39

‘ 3’ stands alone

The required number  =  3 

We can now test our answer to see if this number multiplied by 27 will give a perfect square.

27 × 3 = 81.

Our answer is correct because 81 = 9 × 9 which is a perfect square.

Worked Example 2.3.2:

Find the smallest number by which the following numbers must be multiplied to give perfect squares.

a. 240
b. 45
c. 162

Solution

a. 240

Step 1:

Screenshot 2023 08 20 at 04.46.33

240  =  2 × 2 × 2 × 2 × 3 × 5

Step 2:

Screenshot 2023 08 20 at 04.50.17

The required number  = 3 × 5

=  15

b. 45

Step 1:

Screenshot 2023 08 20 at 04.52.27

45 = 3 × 3 × 5

Step 2: 

Screenshot 2023 08 20 at 04.54.22

Required number  =  5.

c. 162

Step 1:

Screenshot 2023 08 20 at 04.58.05

Step 2:

Screenshot 2023 08 20 at 05.00.50

2 has no pair. The required number  = 2

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