Square Root of 1417
2026-02-28 08:29 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1417

The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square numbers for the given number. Let us now learn how to find the square root using the long division method, step by step:

Step 1: To begin with, we need to group the numbers from right to left. In the case of 1417, we can group it as 17 and 14.

Step 2: Now we need to find n whose square is less than or equal to 14. We can say n is 3 because 3 x 3 = 9, which is less than 14. Now the quotient is 3, and after subtracting 9 from 14, the remainder is 5.

Step 3: Now let us bring down 17, making the new dividend 517. Add the old divisor (3) with itself to get 6, which will be part of our new divisor.

Step 4: The new divisor will be 6n, where n is a digit such that 6n x n is less than or equal to 517. Let us try n = 8, then 68 x 8 = 544, which is too large. Try n = 7, then 67 x 7 = 469, which is less than 517.

Step 5: Subtract 469 from 517, and the remainder is 48. The quotient is now 37.

Step 6: Since the remainder is not zero, add a decimal point to the quotient, and bring down two zeros to make the new dividend 4800.

Step 7: The new divisor is 674 (67 doubled plus 4), and we find a new digit n such that 674n x n is less than or equal to 4800. Let n be 7, then 6747 x 7 = 4729.

Step 8: Subtract 4729 from 4800, the remainder is 71, and the quotient is 37.7.

Step 9: Continue doing these steps until we get two digits after the decimal point.

The square root of √1417 is approximately 37.65.