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.

135

Square root of 135 = 11.6189

Third decimal place = 11.619 (round figure of 11.618)

Second decimal place = 11.62 (round figure of 11.61)

One decimal place = 11.6

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 (1² < 1 < 2²). Take this number as the divisor and the quotient with number under extreme left bar as the dividend. Divide and get the remainder.(0 in this case)

Step 3. Bring down the number under the next bar(i.e.,35 in this case) to the right of the remainder. So the new dividend is 35.

Step 4. Double the divisor and place this digit at ten’s place of new divisor (1+1 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 21 × 1 = 21. Get the remainder.

Step 6. 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 1400. Put a decimal in quotient.

Step 7. Double the divisor and place this digit at ten’s place of new divisor (21+1 in this case).

Step 8. 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 226 × 6 = 1356. Get the remainder.

Step 9. Bring down the number under the next bar(i.e.,00 in this case) to the right of the remainder. So, new dividend is 4400

Step 10. Double the divisor and place this digit at ten’s place of new divisor (226+6 in this case)

Step 11. 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 2321 × 1 = 2321. Get the remainder.

Step 12. 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 207900

Step 13. Double the divisor and place this digit at ten’s place of new divisor (2321+1 in this case).

Step 14. 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 23228 × 8 = 185824. Get the remainder.

Step 15. 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 2207600

Step 13. Double the divisor and place this digit at ten’s place of new divisor (23228+8 in this case). 116279

Step 14. 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 232369 × 9 = 2091321. Get the remainder.

Step 10. Since the remainder is 116279 and we were required to calculate the square root till 4^th decimal place.

∴ = 11.6189