Square Root of 959
2026-02-28 12:48 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-959

The long division method is particularly useful for non-perfect square numbers. In this method, we should check the closest perfect square number 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 959, we need to group it as 59 and 9.

Step 2: Find n whose square is closest to 9. Here, n can be 3 because 3 x 3 = 9. Now the quotient is 3, and after subtracting 9-9, the remainder is 0.

Step 3: Bring down 59, which is the new dividend. Add the old divisor with itself: 3 + 3 = 6, which will be our new divisor.

Step 4: The new divisor will be 6n. Find the value of n such that 6n x n is less than or equal to 59. Let n be 9, as 69 x 9 = 621, which is too large. Try n = 8, giving 68 x 8 = 544.

Step 5: Subtract 544 from 590 (59 brought down after the initial group), leaving 46.

Step 6: Since the dividend is less than the divisor, we add a decimal point to our quotient and bring down two zeros to continue the long division. The new dividend is now 4600.

Step 7: Find the new divisor, which is 617, and find n such that 617n x n ≤ 4600. Trying n = 7, we get 617 x 7 = 4319.

Step 8: Subtracting 4319 from 4600 gives 281.

Step 9: Continue this process until the desired decimal accuracy is achieved.

So the square root of √959 is approximately 30.956.