Find the approximate value of the square roots of the following numbers up to the second decimal place.

59.03

Square root of 59.03 to second decimal place = 7.68

(1): To find the square root of a decimal number we put bars on the integral part(i.e.,59) of the number in the usual manner. And place bars on the decimal part (i.e.,03) on every pair of digits beginning with the first decimal place. .

(2): Find the largest number whose square is ≤ the number under the extreme left bar (7² <59< 8²). Take this number as the divisor and the quotient with number under extreme left bar as the dividend. Divide and get the remainder.( 10 in this case)

(3): The remainder is 10. Write the number under the next bar(i.e.,03) to the right of this remainder to get, 1003

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

(5): We know that 146 × 6 = 876, ∴ the new digit is 6.

Divide and get the remainder.

(6): The remainder is127. Write the number under the next bar(i.e.,00) to the right of this remainder to get, 12700

(7): Double the divisor and place this digit at ten’s place of new divisor (146+6 in this case).

(8): We know that 1528 × 8 = 1224, ∴ the new digit is 6.

Divide and get the remainder.

(9): The remainder is 476 and we are required to calculate till second decimal place.

∴ = 7.68