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Q.

Find the square root of 8281.


see full answer

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a

81

b

51

c

91

d

101 

answer is C.

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Detailed Solution

Concept: The square root of 8281 must be determined.
Let's try to determine the 8281's prime factors first to help with this.
The number 8281 can be expressed as using the prime factorization method.
{"mathml":"<math class="image_resized" style="width:143px;height:11px"><span style="font-family:Taking out a pair of common factors.
{"mathml":"<math class="image_resized" style="width:104px;height:22px"><img src="data:image/jpeg;base64,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" width="80" height="22" alt=Hence, the correct answer is option 3.
       
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Find the square root of 8281.