Square Root of 651
2026-02-21 20:27 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-651

The long division method is particularly used for non-perfect square numbers. Let us now learn how to find the square root using the long division method, step by step:

Step 1: To begin with, we group the numbers from right to left. For 651, group it as 51 and 6.

Step 2: Find n such that n² ≤ 6. We can say n = 2 because 2 × 2 = 4, which is less than 6. The quotient is 2 and the remainder is 2.

Step 3: Bring down 51, making the new dividend 251. Double the quotient (2), giving a new divisor of 4.

Step 4: Find n such that 4n × n ≤ 251. For n = 6, 46 × 6 = 276, which is more than 251. Trying n = 5, we have 45 × 5 = 225, which fits.

Step 5: Subtract 225 from 251, leaving a remainder of 26. The quotient is now 25.

Step 6: Since the remainder is less than the divisor, we add a decimal point and bring down zeros, making the new dividend 2600.

Step 7: Double the quotient (25), making the new divisor 50, and find n such that 50n × n ≤ 2600. Trying n = 5 gives 505 × 5 = 2525.

Step 8: Subtract 2525 from 2600, leaving the remainder 75. The quotient is now 25.5.

Step 9: Repeat the process until you achieve the desired precision.

The square root of 651 is approximately 25.5147.