We will look at a different method which will enable the student perform the calculations for squares mentally.
1² = 1 = 1
2² = 4 = 1 + 3
3² = 1 +3 + 5
4² = 1 + 3 + 5 + 7
5² = 1 + 3 + 5 + 7 +9
If we want 13², it will be the sum of the First 13 odd numbers.
So, now we know the squares of numbers 25, 30, 35, 40, 45, 50, 55, 60, 65, etc. If we want to find the squares of any other number, we find it using these squares which we already know.
(31)² = 30 is base and (36)² = 35 is base,
Similarly, last digit is 1 = base is preceding it, last digit is 6 = base is preceding it.
(31)² = (30)² + (30 + 31) = 900 + 61 = 961
(36)² = (35)² + (35 + 36) = 1225 + 71 = 1296
(41)² = (40)² + (40 + 41) = 1600 + 81 = 1681
(46)² = (45)² + (45 + 46) = 2025 + 91 = 2116
(121)² = (120)² + (120 + 121) = 14400 + 241 = 14641
(126)² = (125)² + (125 + 126) = 15625 + 251 = 15876
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