JSS2: MATHEMATICS  1ST TERM

Properties of Whole Numbers I  Week 14 Topics1 Quiz

Properties of Whole Numbers II  Week 24 Topics1 Quiz

Properties of Whole Numbers III  Week 35 Topics1 Quiz

Indices  Week 42 Topics1 Quiz

Laws of Indices  Week 55 Topics1 Quiz

Whole Numbers & Decimal Numbers  Week 64 Topics1 Quiz

Standard Form  Week 73 Topics1 Quiz

Significant Figures (S.F)  Week 84 Topics1 Quiz

Fractions, Ratios, Proportions & Percentages I  Week 96 Topics1 Quiz

Fractions, Ratios, Proportions & Percentages II  Week 104 Topics1 Quiz

Fractions, Ratios, Proportions & Percentages III  Week 113 Topics1 Quiz

Approximation & Estimation  Week 121 Topic1 Quiz
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Perfect Square
A perfect square is a whole number whose square root is a whole number. Examples
9 = 3 x 3…………… \(\scriptsize \sqrt{9}\) = 3
4 = 2Â x 2…………… \(\scriptsize \sqrt{4}\) = 2
1 = 1 x 1…………… \(\scriptsize \sqrt{1}\) = 1
16 = 4 xÂ 4…………… \(\scriptsize \sqrt{16}\)= 4
25 = 5Â x 5…………… \(\scriptsize \sqrt{25}\) = 5
36 = 6Â 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.
Step 2: Pick the product of prime factors in pairs of the same digits. Then multiply digits without pairs (standalone digits) together. This gives the required number. i.e
â€˜ 3â€™ 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 multipliedÂ to give perfect squares.
a. 240
b. 45
c. 162
Solution
a. 240
Step 1:
240 = 2 x 2 x 2 x 2 x 3 x 5
Step 2:
The required number = 3 x 5
= 15
b. 45
Step 1:
45 = 3 x 3 x 5
Step 2:Â 45 =Â (3 x 3) x 5 >Â No pair
Required number = 5.
c. 162
Step 1:
Step 2:
2 has no pair. The required number = 2
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