Question

Find the square root of 1369.
$
  A.{\text{ 31}} \\
  B.{\text{ 33}} \\
  C.{\text{ 36}} \\
  D.{\text{ 37}} \\
$

Answer 1

Hint: In this question factorize the given number and make the factors in square form so use these concepts to reach the solution of the question.

Complete step-by-step answer:

Given number is 1369.
Now we have to find out the square root of this number.
i.e. $\sqrt {1369} $ .
This is also written as ${\left( {1369} \right)^{\dfrac{1}{2}}}$……… (1)
So first factorize the given number,
$ \Rightarrow 1369 = 37 \times 37 = {\left( {37} \right)^2}.$
As we know 37 is a prime number so we cannot further factorize it.
So substitute this value in equation (1) we have,
$ \Rightarrow {\left( {1369} \right)^{\dfrac{1}{2}}} = {\left( {{{\left( {37} \right)}^2}} \right)^{\dfrac{1}{2}}} = {37^{2 \times \dfrac{1}{2}}} = 37$.
So the required square root of 1369 is 37.
Hence option (d) is correct.

Note: In such types of question the key concept we have to remember is that to find out the square root of any number first of all factorize the number and then make the factors in square form so the power of factors which is in square form is cancel out by the power of square root as above so, the resultant value is the required square root of the given number.