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in Square and Square Root by (49.3k points)
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Find the square root of the following numbers without really calculating

(i) 121
(ii) 256
(iii) 4489
(iv) 60025

1 Answer

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First we will prepare a table by using unit digit of given number to find the possible unit digit in their squares.

Unit place digit number of given number Possible unit digit in square
1 1 or 9
4 2 or 8
5 5
6 4 or 6
9 3 or 7

∵ Unit place digit number = 1
∴ Unit place digit in square root = 1 or 9
leaving 21 remaining digit = 1
∵ 12 = 1 < 22
∴ 121 value of 112
∴ \(\sqrt{121}\) = 11

(ii) 256
∵ Unit place digit = 6
∴ Unit place digit in square root number = 4 or 6
Leaving 56 remaining digit = 2
∵12 < 22 < 22
Value of 256 = 142 or 162
∵ 152 = 225
∴ \(\sqrt{256}\) = 16

(iii) 4489
∵ Unit place digit = 9
∴ Unit place digit in square root = 3 or 7
Leaving 89 remaining digits = 44
∵ 62 < 44 <72
∴ Value of 4489 will be 632 or 672
∵ 652 = 4225
∴ \(\sqrt{4489}\) = 67

(iv) 60025
∵ Unit place of digit = 5
∴ Unit place digit in square root = 5
Leaving 25 remaining number = 600
∵ 242 < 600 < 252
∴value of 60025 will be 2452
∴ \(\sqrt{60025}\) = 245

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