Square Root of 353
2026-02-28 08:33 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-353

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 353, we need to group it as 53 and 3.

Step 2: Now we need to find n whose square is less than or equal to 3. We can say n is ‘1’ because 1 × 1 = 1 which is less than or equal to 3. Now the quotient is 1, after subtracting 3-1, the remainder is 2.

Step 3: Now let us bring down 53 which forms the new dividend 253. Add the old divisor with the same number 1 + 1 to get 2 which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 2n as the new divisor, we need to find the value of n.

Step 5: The next step is finding 2n × n ≤ 253. Let us consider n as 9, now 29 × 9 = 261, which is greater than 253. So we try n as 8, now 28 × 8 = 224.

Step 6: Subtract 253 from 224, the difference is 29, and the quotient is 18.

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 2900.

Step 8: Now we need to find the new divisor that is 189 because 189 × 9 = 1701.

Step 9: Subtracting 1701 from 2900 gives the result 1199.

Step 10: Now the quotient is 18.7.

Step 11: Continue these steps until the desired decimal places are achieved.

So the square root of √353 ≈ 18.79.