Square Root of 3.02
2026-02-21 20:28 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-3.02

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 3.02, we need to consider it as 3.02.

Step 2: Now we need to find n whose square is closest to 3. In this case, n is 1 because 1 × 1 is less than or equal to 3. Now the quotient is 1 after subtracting 1 from 3, the remainder is 2.

Step 3: Bring down the next number 02, making it 202. 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 such that 2n × n is less than or equal to 202.

Step 5: The next step is finding 2n × n ≤ 202. Let us consider n as 7, now 2 × 7 × 7 = 196.

Step 6: Subtract 196 from 202, the difference is 6, and the quotient is 1.7.

Step 7: Since we have only one decimal place, continue the process by bringing down two zeroes. Now the new dividend is 600.

Step 8: Now, we need to find the new divisor. Using 34 as the new divisor, 34 × 8 = 272.

Step 9: Subtracting 272 from 600 we get the result 328.

Step 10: Now the quotient is 1.73.

Step 11: Continue doing these steps until we get the desired number of decimal places or the remainder becomes zero.

So the square root of √3.02 is approximately 1.738.