Question

Find the square root of: 8281
A. 41
B. 71
C. 91
D. 111

Answer 1

Hint: Square root of a number is a value, which on multiplied by itself gives the original number. Suppose, ‘x’ is the square root of ‘y’, then it is represented as \[x = \sqrt y \] or we can express the same equation as \[{x^2} = y\] . Here we can see that 8281 is a perfect square. To solve this we factorize the given number.

Complete step by step solution:
Given,
 \[\sqrt {8281} \]
8281 can be factorized as,
 \[8281 = 1 \times 7 \times 7 \times 13 \times 13\]
We can see that 7 is multiplied four times and 13 is multiplied 2 times, we multiply that we get,
 \[8281 = 49 \times 169\] .
Then,
 \[ \Rightarrow \sqrt {8281} = \sqrt {49 \times 169} \]
Since we know that 49 and 169 is a perfect square we can take this outside of the square root we have,
 \[ \Rightarrow \sqrt {8281} = 7 \times 13\]
 \[ \Rightarrow \sqrt {8281} = 91\]
Hence the correct answer is option is (c).
So, the correct answer is “Option C”.

Note: Here \[\sqrt {} \] is the radical symbol used to represent the root of numbers. The number under the radical symbol is called radicand. The positive number, when multiplied by itself, represents the square of the number. The square root of the square of a positive number gives the original number. To find the factors, find the smallest prime number that divides the given number and divide it by that number, and then again find the smallest prime number that divides the number obtained and so on. The set of prime numbers obtained that are multiplied to each other to form the bigger number are called the factors.