Question
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b) Let’s take a number 260 .
(i) Find the square root of 260 by division method.
(ii) What is the remainder left in this process?
(iii) Subtract the remainder from 260 . Is the difference a perfect square?

Ask by Warner Burns. in Nepal
Dec 26,2024

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Answer

  • (i) The square root of 260 is approximately 16 with a remainder of 4.
  • (ii) The remainder is 4.
  • (iii) Subtracting the remainder from 260 gives 256, which is a perfect square.

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Beyond the Answer

To find the square root of 260 using the division method, pair the digits starting from the decimal point. The pairs are (2)(60). The largest square less than or equal to 2 is 1 (1x1), so write 1 (the divisor) under 2, subtract it to get 1, and bring down the next pair (60) making it 160. Now double the 1 (making it 2) and find a digit ‘x’ such that 2x * x <= 160. You find x = 7 (27 * 7 = 189 exceeds it). So we try 6. 26 * 6 = 156 gives a valid result. Subtract 156 from 160 to get a remainder of 4.
After subtracting the remainder (4) from 260, we get 256, which is indeed a perfect square since 16 x 16 = 256! So, yay for math celebrations! 🎉

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