The division method is a technique used to find the square root of numbers, especially larger ones or those with unknown values. This method is efficient and accurate. The YouTube video, Finding Square root by division method, explains the process, and this answer will outline it step by step.
Steps for Finding Square Roots Using the Division Method:
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Pair the Digits: Start by grouping the digits of the number you want to find the square root of into pairs, starting from the right. If there's an odd number of digits, the leftmost single digit is considered a pair by itself.
- Example: For the number 12345, the pairs will be 1, 23, and 45. For the number 9876, the pairs will be 98 and 76.
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Set up the Division: Draw a division symbol like you would for long division. Write the number whose square root you're finding beneath the division symbol, leaving space above.
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Find the First Divisor: Look for the largest number whose square is less than or equal to the leftmost pair (or single digit). Write this number as the first digit of the square root above the division symbol and also as the divisor on the left of the division symbol.
- For example, if the leftmost pair is 12, the number is 3 because 3 3 = 9, and 4 4 = 16 which is greater than 12.
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Multiply and Subtract: Multiply the number on top by itself (the divisor). Write the result beneath the leftmost pair and subtract it.
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Bring Down the Next Pair: Bring down the next pair of digits next to the remainder from the previous step.
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Find the New Divisor: Now, you must find the next digit of the square root. Double the current quotient (number written above the division symbol) and write it down leaving a blank space to add a new digit to create new divisor. Then, find the largest digit to fit in both the blank space in the divisor and the next digit for the quotient, such that when the new divisor is multiplied by this digit, the product is less than or equal to the current dividend (remainder from step 4 combined with the brought down number from step 5). Write the new digit as the next digit of the square root and beside the doubled number for divisor.
- If the remainder from step 4 combined with the brought down number from step 5 is 334, and your current quotient is 3 and 6 is the new digit, your new divisor will be 66. Hence 66 6 = 396 which is more than 334 so we will try with 5. 65 5= 325 is less than 334. Hence, we will continue with 5.
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Repeat: Repeat steps 4 through 6 until all pairs have been used. If you want to find the square root to a decimal place, add pairs of zeros and repeat the process as needed.
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The Result: The final number written above the division symbol is the square root.
Example: Square Root of 625
- Pairing: 6 and 25
- Setup:
______ √6 25 - First Divisor: The largest square less than or equal to 6 is 2 (2 * 2 = 4).
2____ √6 25 4 - Multiply and Subtract: 6 - 4 = 2
2____ √6 25 4 -- 2 - Bring Down Pair: Bring down 25
2____ √6 25 4 -- 2 25 - Find New Divisor: Double the quotient (2), which is 4. Now find a digit such that 4[digit] [digit] is less than or equal to 225. Try 5: 45 5 = 225
2 5 √6 25 4 -- 2 25 2 25 ---- 0 - Final Result: The square root of 625 is 25.
