Square Root of 1504
2026-02-28 17:42 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1504

The long division method is particularly used 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 1504, we need to group it as 04 and 15.

Step 2: Now we need to find n whose square is less than or equal to 15. We can say n is '3' because 3 × 3 = 9 is less than 15. Now the quotient is 3, and after subtracting 9 from 15, the remainder is 6.

Step 3: Bring down 04 to make it 604 as the new dividend. Add the old divisor with the same number 3 + 3 = 6 which will be our new divisor.

Step 4: Find a digit x such that 6x × x is less than or equal to 604. Let’s choose x as 9, now 69 × 9 = 621, which is too large, so we try x as 8, giving us 68 × 8 = 544.

Step 5: Subtract 544 from 604, the difference is 60, and the quotient is 38.

Step 6: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 6000.

Step 7: Find the new divisor which is 769 because 769 × 7 = 5383.

Step 8: Subtract 5383 from 6000, we get the result 617.

Step 9: Now the quotient is 38.7.

Step 10: Continue doing these steps until we get the desired decimal places.

So, the square root of √1504 ≈ 38.77886.