Question

Find the square root of $1764$ by the division method.

Answer 1

Square root of $1764$ by the division method:

The given number is $1764$.

We group the numbers as $17,64$.

Place a bar over every pair of digits starting from the digit at one’s place. If the number of digits is odd, then the left-most single-digit also will have a bar.

Step $1$: Consider $17$

Find the largest number whose square is less than or equal to the number under the extreme left bar ($17$).

We get $4$ here. Take this number as the divisor and the quotient with the number under the extreme left bar as the dividend. Divide and get the remainder. Now the quotient is $4$. The remainder is 1.

Step $2$: Bring down $64$.

Double the divisor and enter it with a blank on its right. It becomes $8\_\_$.

Guess the largest possible digit to fill the blank which will also become the new digit in the quotient, such that when the new divisor is multiplied to the new quotient the product is less than or equal to the dividend. In this case, it is $82\times 2$. So we choose a new digit as $2$. Get the remainder.

Since the remainder is $0$ and no digits are left in the given number the square root of $1764$ is $42$.

Hence, the square root of $1764$ is $42$.