The square root of 53361 is:

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231

211

261

249

answer is A.

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Detailed Solution

Concept- A number can be expressed as the product of its prime factors to find its square root. This is how prime factorization is done. Once the number has been expressed as the product of its prime factors, begin by creating pairs of prime factors and counting each pair once to obtain the square root.
The number 53361 can be divided by 9 because its digit sum, 5+3+3+6+1=18, is divisible by 9, and 9 is the result of two 3s. Therefore, 53361 may be expressed as 53361=3×3×5929. Due to its odd nature, the number 5929 is currently not divisible by 2 and its digit sum is not divisible by 3. The following prime on the list is therefore 7, and 5929 can be divided by 7. As a result, 53361 can be written as 53361=3×3×7×847 and we are aware that when 847 is divided by 7, the residual is zero and the quotient is 121. Furthermore, the square of 11 is 121.
As a result, 53361 can be written as:

53361 = 3 \times 3 \times 7 \times 7 \times 11 \times 11

Hence, the correct answer is option 1) 231

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