You use long division.
Find the largest number whose square is less than or equal to the number in the leftmost group (55 < 30 < 66). Take this number as the divisor and the quotient with the number in the leftmost group as the dividend (30). Divide and get the remainder (5 in this case).
Bring down the next pair 58. Add the divisor with the quotient and enter it with a blank on its right. Guess a largest possible digit to fill the blank which will also become the new digit in the quotient, such that when the new divisor is multiplied to the new quotient the product is less than or equal to the dividend. In this case 105 × 5 = 525, so we choose the new digit as 5. Get the remainder.
Bring down the next pair 09. Add the divisor with the quotient and enter it with a blank on its right. Guess a largest possible digit to fill the blank which will also become the new digit in the quotient, such that when the new divisor is multiplied to the new quotient the product is less than or equal to the dividend. In this case 1103 × 3 = 3309, so we choose the new digit as 3. Get the remainder.
Put the decimal point.
End of division (Remainder is 0 and next digit after decimal is 0).
√305809 = 553
