How to Find the Square Root of a Number

Finding the square root of a number involves determining a value that, when multiplied by itself, gives the original number. Here are the steps to find the square root:

  1. Understand the Concept: The square root of a number n is a value x such that x * x = n. For example, the square root of 16 is 4 because 4 * 4 = 16.
  2. Prime Factorization Method:
    • Break down the number into its prime factors.
    • Pair the prime factors.
    • Multiply one number from each pair to get the square root.

    Example: To find the square root of 36, factorize it into 2 * 2 * 3 * 3. Pair them as (2 * 2) and (3 * 3). Multiply one number from each pair: 2 * 3 = 6. So, the square root of 36 is 6.

  3. Long Division Method:
    • Group the digits of the number in pairs, starting from the decimal point.
    • Find the largest number whose square is less than or equal to the first group.
    • Subtract the square of this number from the first group and bring down the next pair of digits.
    • Double the divisor and find a digit to place in the quotient such that the new divisor multiplied by this digit is less than or equal to the current dividend.
    • Repeat the process until you reach the desired precision.

    Example: To find the square root of 144, use the long division method to get 12 as the square root.

  4. Using a Calculator: For quick results, you can use a calculator. Simply enter the number and press the square root button (√) to get the result.

These methods help you find the square root of a number manually or using tools. Choose the method that best suits your needs.

More Related Questions