Question
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?
(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
Upstudy AI Solution
Tutor-Verified Answer
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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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! 🎉