Find the square root of 2209.

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answer is A.

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Detailed Solution

Concept: The simplest method to determine the square roots of any number is to use the synthetic division procedure. First, we must take the last two integers as a pair and identify the number whose square will make up that pair. The numbers that can be squared to create this number in this case, 09, are 3 and 7. So, starting with 7, we shall split the number. If there are more than one number that can create a pair by squaring, we can use the hit-and-miss approach. Therefore, we can divide by three and check the outcome, and so on.
We'll split in the manner that synthetic division typically occurs. However, each time a number is divided by another, the result is also added to the original divisor. The result of the addition will act as our new divisor. This procedure is repeated until either no leftovers are left at all or there is a very small leftover that cannot be separated further. As a result, the quotient will only provide the right answer if there is no residue.