Question

Find the square root of the following number by division method: 28224

Answer 1

Hint: Use the steps of the square root by long division method to find the square root of a given problem.

Complete step-by-step answer:
In the question we have to find the square root of the number 28224 by division method.
First, we write the steps of doing the Long division method for finding square roots.
Step 1: First group the digits in pairs, starting with the digit in units place. Each pair and the remaining digit (if any) is called a period.
Step 2: Think of the largest number whose square is equal to or just less than the first period. Taking this number as a divisor and also the quotient.
Step 3: Subtract the product of the divisor and the quotient from the first period and bring down the next period to the right of the remainder. This makes a new dividend.
Step 4: Now, the new divisor is obtained by taking two times the quotient and assessing the suitable digit which is also taken as the next digit of quotient, chosen in such a way that the product of the new divisor and the digits is equal or just less than the new dividend.
Step 5: Repeat steps (2), (3), (4) till all the periods have been taken up. Now the quotient so obtained is the required square root of the given number.
Let's take an example of finding square root of 784.

Here square root is 28.
Now let’s take the number 28224

So, the square root of number 28224 is 168.
The answer is 28224

Note: Students generally don’t know clearly how to do square root by division method, hence they should follow the steps in the solution so that the concept becomes clear. They should also do calculations clearly to avoid any errors.