Find the square root of 42.25 using long division method.

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Set up problem: Set up the problem in long division format. Place 42.25 under a square root symbol, which is similar to a long division symbol. Group the digits in pairs, starting from the decimal point and moving to the left and to the right. For 42.25, we have two pairs: 42 and 25.Find largest square number: Find the largest square number less than or equal to the first pair (42). The largest square number less than or equal to 42 is 36 because 6 * 6 = 36.Subtract square number: Subtract the square number (36) from the first pair (42) to get the remainder. 42 - 36 = 6. Bring down the next pair of digits (25) next to the remainder to get 625.Double and form new divisor: Double the divisor (6) and write it down with a blank digit on its right to form a new divisor. Doubling 6 gives us 12, and we write it as 12_ with a blank digit to find out.Determine largest digit: Determine the largest digit (X) that fits in the blank of 12X such that 12X * X is less than or equal to 625. The largest value for X that satisfies 12X * X <= 625 is 5 because 125 * 5 = 625.Subtract product from remainder: Subtract the product of the new divisor and the new digit from the remainder. 625 - (125 * 5) = 625 - 625 = 0. There is no remainder.Write down result: Write down the result. The result of the square root of 42.25 is the combination of the digits found in Steps 2 and 5, which are 6 and 5 respectively.

Find the square root of $42.25$ using long division method.

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Find the square root of $42.25$ using long division method.