Square Root of 9375
2026-02-28 08:38 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-9375

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 9375, we need to group it as 75 and 93.

Step 2: Now we need to find n whose square is ≤93. We can say n as ‘9’ because 9 x 9 is less than or equal to 93. Now the quotient is 9; after subtracting 81 from 93, the remainder is 12.

Step 3: Now let us bring down 75, which is the new dividend. Add the old divisor with the same number 9 + 9; we get 18, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 18n as the new divisor; we need to find the value of n.

Step 5: The next step is finding 18n x n ≤ 1275. Let us consider n as 7. Now, 18 x 7 x 7 = 1764. Since 1764 is greater than 1275, try n as 6.

Step 6: With n as 6, 18 x 6 x 6 = 1296. Subtracting 1296 from 1275 is not possible as 1296 is greater, so n has to be decreased.

Step 7: With n as 5, 18 x 5 x 5 = 1125. Subtract 1125 from 1275; the difference is 150, and the quotient is 95.

Step 8: Now, since the number of digits in the dividend is less than the divisor, we add a decimal point to continue with zeros. Now, the new dividend is 15000.

Step 9: The next divisor is 1950, as 195 x 9 = 1755.

Step 10: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal value, continue till the remainder is zero.

So, the square root of √9375 ≈ 96.87