Square Root of 498
2026-02-28 19:13 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-498

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 498, we need to group it as 98 and 4.

Step 2: Now we need to find n whose square is 4. We can say n as ‘2’ because 2^2 = 4, which is lesser than or equal to 4. Now the quotient is 2; after subtracting 4 from 4, the remainder is 0.

Step 3: Now let us bring down 98, which is the new dividend. Add the old divisor with the same number 2 + 2; we get 4, which will be our new divisor.

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

Step 5: The next step is finding 4n × n ≤ 98. Let us consider n as 2; now 4 x 2 x 2 = 16.

Step 6: Subtract 98 from 16; the difference is 82, and the quotient is 22.

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 zeros to the dividend. Now the new dividend is 8200.

Step 8: Now we need to find the new divisor. Let us consider n as 9, because 449 x 9 = 4041.

Step 9: Subtracting 4041 from 8200, we get the result 4159.

Step 10: Now the quotient is 22.9.

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 √498 ≈ 22.29.