JSS2: MATHEMATICS - 1ST TERM
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Properties of Whole Numbers I | Week 14 Topics|1 Quiz
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Properties of Whole Numbers II | Week 24 Topics|1 Quiz
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Properties of Whole Numbers III | Week 35 Topics|1 Quiz
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Indices | Week 42 Topics|1 Quiz
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Laws of Indices | Week 55 Topics|1 Quiz
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Whole Numbers & Decimal Numbers | Week 64 Topics|1 Quiz
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Standard Form | Week 73 Topics|1 Quiz
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Significant Figures (S.F) | Week 84 Topics|1 Quiz
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Fractions, Ratios, Proportions & Percentages I | Week 96 Topics|1 Quiz
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Fractions, Ratios, Proportions & Percentages II | Week 104 Topics|1 Quiz
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Fractions, Ratios, Proportions & Percentages III | Week 113 Topics|1 Quiz
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Approximation & Estimation | Week 121 Topic|1 Quiz
Perfect Square
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.

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.

‘ 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:

240 = 2 × 2 × 2 × 2 × 3 × 5
Step 2:

The required number = 3 × 5
= 15
b. 45
Step 1:

45 = 3 × 3 × 5
Step 2:

Required number = 5.
c. 162
Step 1:

Step 2:

2 has no pair. The required number = 2