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.

777

Square root of 777 = 27.8747

Third decimal place = 27.875 (round figure of 27.874)

Second decimal place = 27.88 (round figure of 27.87)

One decimal place = 27.9 (round figure of 27.8)

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 (2² < 7 < 3²). Take this number as the divisor and the quotient with number under extreme left bar as the dividend. Divide and get the remainder.(3 in this case)

Step 3. Bring down the number under the next bar(i.e.,77 in this case)to the right of the remainder. So the new dividend is 377.

Step 4. Double the divisor and place this digit at ten’s place of new divisor (2+2 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 47 × 7 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 4800. Put a decimal in quotient.

Step 7. Double the divisor and place this digit at ten’s place of new divisor (47+7 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 548 × 8 = 4384. 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 41600

Step 10. Double the divisor and place this digit at ten’s place of new divisor (548+8in 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 5567 × 7 = 38969. 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 263100

Step 13. Double the divisor and place this digit at ten’s place of new divisor (5567+7 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 55744 × 4 = 222976. 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 4012400

Step 16. Double the divisor and place this digit at ten’s place of new divisor (55744+4 in this case).

Step 17. 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 557487 × 7 = 3902409 Get the remainder.

Step 18. Since the remainder is 109991 and we were required to calculate

the square root till 4^th decimal place.

∴ = 27.8747