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JSS2: MATHEMATICS - 1ST TERM

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  1. Properties of Whole Numbers I | Week 1
    4Topics
    |
    2 Quizzes
  2. Properties of Whole Numbers II | Week 2
    4Topics
    |
    2 Quizzes
  3. Properties of Whole Numbers III | Week 3
    4Topics
    |
    1 Quiz
  4. Indices | Week 4
    2Topics
    |
    1 Quiz
  5. Laws of Indices | Week 5
    5Topics
    |
    1 Quiz
  6. Whole Numbers & Decimal Numbers | Week 6
    4Topics
    |
    1 Quiz
  7. Standard Form | Week 7
    3Topics
    |
    1 Quiz
  8. Significant Figures (S.F) | Week 8
    4Topics
    |
    1 Quiz
  9. Fractions, Ratios, Proportions & Percentages I | Week 9
    6Topics
    |
    1 Quiz
  10. Fractions, Ratios, Proportions & Percentages II | Week 10
    4Topics
    |
    1 Quiz
  11. Fractions, Ratios, Proportions & Percentages III | Week 11
    3Topics
    |
    1 Quiz
  12. Approximation & Estimation | Week 12
    1Topic
    |
    1 Quiz
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A perfect square is a whole number whose square root is a whole number.  Examples

9 = 3 x 3…………… \(\scriptsize \sqrt{9}\) = 3

 4 = 2  x 2…………… \(\scriptsize \sqrt{4}\) = 2

 1 = 1 x 1…………… \(\scriptsize \sqrt{1}\) = 1

 16 = 4 x  4…………… \(\scriptsize \sqrt{16}\)= 4

 25 = 5 x 5…………… \(\scriptsize \sqrt{25}\) = 5

 36 = 6  x 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.

Example 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.

Screen Shot 2020 11 22 at 8.15.33 AM

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

Screen Shot 2020 11 22 at 8.15.44 AM

‘ 3’  is  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 x 3 = 81. Our answer is correct because 81 = 9 x 9 which is a perfect square.

Example 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:

Screen Shot 2020 11 22 at 8.22.45 AM

240  =  2 x 2 x 2 x 2 x 3 x 5

Step 2:

Screen Shot 2020 11 22 at 8.23.21 AM

The required number  = 3 x 5

=  15

b. 45

Step 1:

Screen Shot 2020 11 22 at 8.55.12 AM

45 = 3 x 3 x 5

Step 2:  45 =  (3 x 3) x 5 > No pair

Required number  =  5.

c. 162

Step 1:

Screen Shot 2020 11 22 at 8.54.53 AM

Step 2:

Screen Shot 2020 11 22 at 9.02.10 AM

2 has no pair. The required number  = 2

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