Question

Find square root of 1089 by first principle method (Vargamula method)
(A) 19
(B) 23
(C) 29
(D) 33

Answer 1

Hint: Square root of a perfect square by the long division method
When numbers are very large, the method of finding their square roots by factorisation becomes lengthy and difficult.
So, we use the long division method which is explained in the following steps –
Step-1
Group the digits in pairs, starting with the digit in the 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. Take this number as the divisor and also as 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 becomes the new dividend.
Step-4
Now, the new divisor is obtained by taking two times the quotient and annexing with it a suitable digit which is also taken as the next digit of the quotient, chosen in such a way that the product of the new divisor and this digit is equal to or just less than the new dividend.
Step-5
Repeat steps 2, 3 and 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 solve the given question by using these steps one by one.

Complete answer:
We need to find root of 1089

1) We will make pairs from digits. We will get two periods. One from 89 others from 10.
2) Think of a whole number whose square is equal or just less than 10.
     On trial it is 3. Take 3 as a divisor, square it and put it below 10.
    Write subtraction of 10 and 9 in the remainder section.
3) So, $10 - 9 = 1$
         1 is the remainder.
        We will write next period 89 to the right of remainder.So our new dividend is 189.
4) Now taking two times the quotient which is $3 \times 2 = 6$ and annexing with it a suitable number
    i.e., 3.
   3 will be the next digit of quotient also.
  The new divisor is 63 and the next digit in quotient is 3.
$63 \times 3 = 189$
5) Write this 189 from the new dividend i.e., 189 also.
     $189 - 189 = 0$
6) So remainder is 0 therefore the quotient is our required answer.
7) Therefore the square root of 1089 is 33.

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