Square Root of 1515
2026-02-28 10:37 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1515

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 1515, we need to group it as 15 and 15.

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

Step 3: Now let us bring down the next group, which is 15, making the new dividend 615. Add the old divisor with the same number 3 + 3 = 6, which will be our new divisor.

Step 4: The new divisor will be 60n, where n is our next digit in the quotient.

Step 5: Find n such that 60n × n ≤ 615. Let us consider n as 1. Now 601 × 1 = 601.

Step 6: Subtract 601 from 615, the remainder is 14, and update the quotient to 31.

Step 7: Since the dividend is less than the divisor, add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend, making it 1400.

Step 8: Now find the new divisor, which is 620, because 6202 × 2 = 1240.

Step 9: Subtracting 1240 from 1400 gives 160.

Step 10: The quotient is now 38.92.

Step 11: Continue these steps until you get the desired precision.

So the square root of √1515 ≈ 38.923.