Square Root of 1452
2026-02-28 15:52 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1452

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 1452, we need to group it as 52 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 × 3 = 9, which is lesser than or equal to 14. Now the quotient is 3, and after subtracting 9 from 14, the remainder is 5.

Step 3: Now let us bring down 52 which is the new dividend. Add the old divisor with the same number 3 + 3 we get 6 which will be our new divisor with a blank space for the next digit.

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 ≤ 552. Let us consider n as 8, now 68 × 8 = 544.

Step 6: Subtract 552 from 544; the difference is 8, and the quotient is 38.

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 800.

Step 8: Now we need to find the new divisor, which is 761 because 761 × 1 = 761.

Step 9: Subtracting 761 from 800 we get the result 39.

Step 10: Now the quotient is 38.1.

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 √1452 is approximately 38.09.