Square Root of 7900
2026-02-28 23:19 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-7900

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 7900, we need to group it as 79|00.

Step 2: Now we need to find n whose square is less than or equal to 79. We can say n is 8 because 8 x 8 = 64, which is less than 79. Now the quotient is 8 after subtracting 64 from 79; the remainder is 15.

Step 3: Now let us bring down 00, which makes the new dividend 1500. Add the old divisor with the same number: 8 + 8 = 16, which will be our new divisor.

Step 4: Now, find n such that 16n × n ≤ 1500. Let us consider n as 9; now 169 x 9 = 1521, which is larger than 1500, so we consider n as 8.

Step 5: Subtract 1500 from 1456 (168 x 8 = 1456); the difference is 44, and the quotient is 88.

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 zeros to the dividend. Now the new dividend is 4400.

Step 7: Now we need to find the new divisor, which will be 176. Let’s find n such that 176n x n ≤ 4400. Suppose n is 2, then 1762 x 2 = 3524.

Step 8: Subtract 3524 from 4400, we get 876.

Step 9: Now the quotient is 88.8

Step 10: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue until the remainder is zero. So the square root of √7900 ≈ 88.88