Square Root of 7380
2026-02-28 10:03 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-7380

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 7380, we need to group it as 80 and 73.

Step 2: Now we need to find n whose square is less than or equal to 73. We can say n is ‘8’ because 8^2 = 64 is less than 73. Now the quotient is 8, and after subtracting 64 from 73, the remainder is 9.

Step 3: Now let us bring down 80, which is the new dividend. Add the old divisor with the same number 8 + 8 = 16, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 16n as the new divisor, we need to find the value of n.

Step 5: The next step is finding 16n × n ≤ 980. Let us consider n as 5, now 16 x 5 x 5 = 825

Step 6: Subtract 980 from 825; the difference is 155, and the quotient is 85.

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 15500.

Step 8: Now we need to find the new divisor that is 859 because 859 x 9 = 7731

Step 9: Subtracting 7731 from 15500, we get the result 7779.

Step 10: Now the quotient is 85.9

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal values, continue till the remainder is zero. So the square root of √7380 is approximately 85.91.