Square Root of 94
2026-02-28 08:55 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-94

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 94, we need to consider it as 94 itself.

Step 2: Now we need to find n whose square is 81. We can say n as ‘9’ because 9 x 9 is lesser than or equal to 94. Now the quotient is 9, and after subtracting 81 from 94, the remainder is 13.

Step 3: Now let us bring down 00 to make it 1300 as the new dividend. Add the old divisor with the same number 9 + 9 to get 18, which will be our new divisor.

Step 4: The new divisor will be 18n, where we need to find the value of n such that 18n x n ≤ 1300. Let us consider n as 7, now 187 x 7 = 1309, which is too large, so we try n as 6.

Step 5: Subtract 187 x 6 = 1122 from 1300, the difference is 178, and the quotient is 9.6.

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 zeroes to the dividend. Now the new dividend is 17800.

Step 7: Find the new divisor which is 192 (from 186 and 6), because 1926 x 6 = 11556. Step 8: Subtract 11556 from 17800, we get the result 6244.

Step 9: Now the quotient is 9.69. Step 10: 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 √94 is approximately 9.69.