To find the square root of using the long division method, we group digits into pairs, find the largest perfect square less than or equal to the current group, and iteratively double the divisor to calculate subsequent decimal places. The approximate value of 6the square root of 6 end-root is 2.4492.449 . Below is the step-by-step breakdown of the process. 1. Set up the Groups Group digits: Place a decimal point after and add pairs of zeros. Format: Write it as 2. Find the First Digit
Evaluate: Find the largest perfect square less than or equal to Select: The largest perfect square is Subtract: Place on top and on the left. Multiply Remainder: Subtract to get a remainder of 3. Calculate the First Decimal Place Drop down: Bring down the first pair of zeros to make the new number Double divisor: Double the current quotient (
) and place it in the divisor spot with a blank next to it ( Test digits: Find a digit (too high) Update: Choose in the quotient (after the decimal) and next to the Remainder: Subtract 4. Calculate the Second Decimal Place
Drop down: Bring down the next pair of zeros to make the number
Double divisor: Double the entire current quotient ignoring the decimal ( Test digits: Find a digit (too high) Update: Choose . Place it in the quotient and next to Remainder: Subtract 5. Calculate the Third Decimal Place
Drop down: Bring down the final pair of zeros to make the number 4640046400 Double divisor: Double the current quotient ( Test digits: Find a digit Update: Choose . Place it in the quotient. Remainder: Subtract 4400144001 4640046400 Summary Table of Long Division Quotient Digit 4640046400 ✅ Final Answer The square root of
calculated up to three decimal places using the long division method is exactly 2.4492.449
If you want to explore further, tell me if you would like to: Calculate more decimal places for 6the square root of 6 end-root Learn how to find the square root of another number See a geometric proof of square roots
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