Square Root of 313
2026-02-28 01:29 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-313

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 313, we need to group it as 13 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 is lesser than or equal to 3. Now the quotient is 1, after subtracting 1 from 3 the remainder is 2.

Step 3: Now let us bring down 13 which is the new dividend. Add the old divisor with the same number 1 + 1, we get 2 which will be our new divisor.

Step 4: Find a digit n such that 2n × n is less than or equal to 213. The suitable n is 8, giving us 28 × 8 = 224.

Step 5: Subtract 213 from 224, the difference is -11, and the quotient is 18.

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 1100.

Step 7: The new divisor becomes 36, and the divisor times the next digit should be less than or equal to 1100. Using 3, 363 × 3 = 1089.

Step 8: Subtracting 1089 from 1100, we get 11.

Step 9: Continue this process until you have the desired decimal places in the quotient.

The square root of √313 ≈ 17.691.