Question

How do you find $\sqrt {1521} $?

Answer 1

Hint: To solve this we need to know the square of the number $3$ and what are all the squares of the number from $1$ to $10$ that ends with $1$. With this we are able to find the answer for this question for the given number.

Complete step by step solution:
This method which I am going to tell in this, is a trick to find the square root of any number. To do this trick, one has to know the square of the number from $1$ to $10$. Let’s move on to the problem.
Consider the question,
$\sqrt {1521} $

First, we need to look at the unit digit of the number and here the unit digit is $1$. And now pick the square number between $1$ and $10$ which ends with one, which is $1$ and $9$. Square of $1$ will be $1$ and square of 9 will be 81. Now write the number as,
$
  \_1 \\
  \_9 \\
 $
Here our answer either should end with $1$ or $9$, there is only two possibilities and to find this we have to consider the given question which is,
$\sqrt {1521} $

Now cancel the last two digits of a number and consider the other number which is $15$, now pick the square of the number from $1$ to $10$ so that the number should be nearly lesser than $15$. And the number will be $3$, if we square $3$ we will get $9$, which is nearly lesser than $15$. Now we can write,
$
  31 \\
  39 \\
 $

The answer for our question should be any one of these two number and to confirm this, we try to find the square of $35$, which is $1225$ and now the given question $\sqrt {1521} $ is greater than $1225$ and our required answer is $39$.

Note: While finding the root of any number, if we check the units digit, or sometimes the last two digits together, a lot of trial and error process gets cut down, as we will be able to identify with the divisibility rule which short lists some numbers to be trailed.