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
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