Finding Square Roots by Division Method
Using the long division algorithm to determine the square root of larger numbers.
Definition
The long division method for finding square roots is an algorithmic procedure used for larger numbers where prime factorization becomes tedious or difficult. It involves pairing digits from right to left, finding the greatest number whose square is less than or equal to the leftmost pair or single digit, and iteratively bringing down pairs while doubling the divisor.
Worked examples
To find sqrt(529), pair digits as 5 29. The largest square less than or equal to 5 is 4 (2^2). Subtracting gives remainder 1, bring down 29 to make 129. Double the divisor 2 to get 4, and trial 43 * 3 = 129, yielding a square root of 23.
To find sqrt(1369), pairing gives 13 69. The greatest square less than 13 is 9 (3^2). Remainder is 4, bring down 69 to make 469. Double 3 to get 6, and trial 67 * 7 = 469, yielding 37.
To find sqrt(2304), pairing gives 23 04. Using the division process yields 48.
Common mistakes
- • Pairing digits from left to right instead of starting from right to left.
- • Failing to double the entire current quotient when forming the new divisor for the next step.
Introduction to Rational Numbers
Rational Numbers
Properties of Rational Numbers
Rational Numbers
Representation on Number Line
Rational Numbers
Rational Numbers Between Two Rational Numbers
Rational Numbers
Algebraic Expressions and Equations
Linear Equations in One Variable
Solving Equations with Variables on Both Sides
Linear Equations in One Variable