Find the square roots of the following numbers to the fourth decimal place by the division method. Then write the approximate value of each square root up to the third, second and first decimal places.

10

Square root of 10 = 3.1622

Third decimal place = 3.162

Second decimal place = 3.16

One decimal place = 3.1

Step 1: Place a bar over every pair of digits starting from the one’s digit

Step 2: Find the largest number whose square is ≤ the number under the extreme left bar (3² < 10 < 4²). Take this number as the divisor and the quotient with number under extreme left bar as the dividend. Divide and get the remainder.(1in this case)

Step 3. Bring down the number under the next bar(i.e.,00 in this case) to the right of the remainder. So the new dividend is 100. Put a decimal in the quotient.

Step 4. Double the divisor and place this digit at ten’s place of new divisor (3+3 in this case)

Step 5. Guess the largest possible digit to fill the unit’s digit of new divisor which also become the new digit in the quotient, such that new divisor is multiplied to the new quotient the product is ≤ the dividend.

In this case 626 × 6 = 3756. Get the remainder.

Step 6. Double the divisor and place this digit at ten’s place of new divisor (626+6 in this case)

Step 7. Guess the largest possible digit to fill the unit’s digit of new divisor which also become the new digit in the quotient, such that new divisor is multiplied to the new quotient the product is ≤ the dividend.

In this case 6322 × 2 = 12644. Get the remainder.

Step 8. Double the divisor and place this digit at ten’s place of new divisor (6322+2 in this case)

Step 9. Guess the largest possible digit to fill the unit’s digit of new divisor which also become the new digit in the quotient, such that new divisor is multiplied to the new quotient the product is ≤ the dividend.

In this case 63242 × 2 = 126484. Get the remainder.

Step 10. Since the remainder is 49116 and we were required to calculate the square root till 4^th decimal place.

∴ = 3.1622