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Find the square root of 225 using “Repeated Subtraction”.
A. 11
B. 15
C. 5
D. 8

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Last updated date: 29th Feb 2024
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IVSAT 2024
Answer
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Hint: Here, we will subtract the consecutive odd numbers i.e. $1,3,5,...$ from the number in every step till we reach 0. The number of steps required to reach 0 will give us the required square root of the given number. The square root of a number is a factor which when multiplied by itself gives the original number.

Complete step by step solution:
According to the question, we are required to find the square root of 225 using “Repeated Subtraction Method” in which we subtract $1,3,5,...$ from the number in every next step till we get a $0$ and the number of steps is equal to the square root of the number.
Hence,
1) $225 - 1 = 224$
2) $224 - 3 = 221$
3) $221 - 5 = 216$
4) $216 - 7 = 209$
5) $209 - 9 = 200$
6) $200 - 11 = 189$
7) $189 - 13 = 176$
8) $176 - 15 = 161$
9) $161 - 17 = 144$
10) $144 - 19 = 125$
11) $125 - 21 = 104$
12) $104 - 23 = 81$
13) $81 - 25 = 56$
14) $56 - 27 = 29$
15) $29 - 29 = 0$
Thus, number of steps $ = $ square root of $225 = 15$
Hence, the square root of 225 is 15.

Therefore, option B is the correct answer.

Note:
An alternate way of solving this question is by using the prime factorization method. Hence, if it was not mentioned to use the given method specifically then we could have preferred that method than using this lengthy one. This is for our knowledge so that we should at least be aware that there is another way as well to solve these types of questions. But it is recommended to use the prime factorization method only if nothing specific is mentioned in the question regarding the method to be used as this could consume a lot of time if the number is not small.