Square Root of 1519
2026-02-28 04:57 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1519

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 1519, we need to group it as 19 and 15.

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

Step 3: Now let us bring down 19, which is the new dividend. Add the old divisor with the same number 3 + 3, we get 6, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 6n as the new divisor, we need to find the value of n.

Step 5: The next step is finding 6n × n ≤ 619. Let us consider n as 9, now 69 × 9 = 621.

Step 6: Subtract 619 from 621, the difference is 2, and the quotient is 39.

Step 7: 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 200.

Step 8: Now we need to find the new divisor that is 798, because 798 × 2 = 1596.

Step 9: Subtracting 1596 from 2000, we get the result 404.

Step 10: Now the quotient is approximately 38.965.

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.

So the square root of √1519 is approximately 38.965.