Question

Find the square root of 841.
$
  {\text{A}}{\text{. 21}} \\
  {\text{B}}{\text{. 28}} \\
  {\text{C}}{\text{. 29}} \\
  {\text{D}}{\text{. 25}} \\
 $

Answer 1

Hint: Here, we will proceed by writing the number whose square root is to be determined in a form of product of the prime factors. These prime factors of a number are the prime numbers by which the number is exactly divisible (i.e., the remainder is 0).

Complete step-by-step answer:

Let the square root of 841 is equal to x i.e., $x = \sqrt {841} {\text{ }} \to {\text{(1)}}$
Let us represent the number 841 in terms of the product of its prime factors.
As, $841 = 29 \times 29$
Here, the number 841 can be written as the product of the prime factor 29 with prime factor 29.
So, the number 841 is equal to the square of the prime number 29 i.e., $841 = {\left( {29} \right)^2}{\text{ }} \to {\text{(2)}}$
Using equation (2) in equation (1), we get
$x = \sqrt {841} = \sqrt {{{\left( {29} \right)}^2}} {\text{ }} \to {\text{(3)}}$
As we know that the square root of the square of a number will be equal to that number.
For any number a, $\sqrt {{{\left( a \right)}^2}} = a$
Using the above concept in equation (3), we get
$x = \sqrt {841} = \sqrt {{{\left( {29} \right)}^2}} = 29$
Therefore, the square root of number 841 is equal to 29.
Hence, option C is correct.

Note: In this particular problem, only two prime factors are there which are the same i.e., 29. But if there occur more than two prime factors of the number whose square root is required, we make the pairs of two prime factors (which are the same) so that we can write that pair as the square of that prime factor and can be taken outside of the square root.