QUESTION

# Explain the steps of finding the square root of 1369 by division method.

Hint- The square root of a number by using a long division method is described in the solution, we first group the digits in the number. Differentiate properly between the period, quotient and remainders and follow the steps mentioned below.

Square root of a perfect square by the long division method
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 i.e, $\overline {13} \overline {69}$, 13 and 69 are periods here.
2. Find the largest number whose square is equal to or just less than the first period.Take this number as the divisor and as the quotient. This number is 3 because 3*3=9
 3 3 $\overline {13} \overline {69}$

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. New dividend is 469.
 3 3 $\overline {13} \overline {69} \\\;\;9$ $\;\;469$

4. Now, the new divisor is obtained by taking two times the quotient ( 3*2) and annexing with it a suitable digit ( which is 7) 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 ( which is 67*7=469) is equal to or just less than the new dividend.
 37 3 $\overline {13} \overline {69} \\\;\;9$ 67 $\;\;469 \\ \;\;469$ $\;\;\;\;0$

∴$\sqrt {1369} = 37$
Note- Finding the square root of a number is the inverse operation of squaring that number. Remember , the square of a number is that number times itself. The perfect squares are the squares of the whole numbers.