Square Root of 5.39
2026-02-28 23:34 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-5.39

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 5.39, we need to group it as 5 and 39.

Step 2: Now we need to find n whose square is less than or equal to 5. We can say n is ‘2’ because 2 x 2 = 4 is less than or equal to 5. Now the quotient is 2, and after subtracting 4 from 5, the remainder is 1.

Step 3: Now let us bring down 39, making it the new dividend. Add the old divisor with the quotient 2 + 2 to 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 ≤ 139. Let us consider n as 3, now 4 x 3 x 3 = 36.

Step 6: Subtract 36 from 139, the difference is 103, and the quotient so far is 2.3.

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 zeroes to the dividend. Now the new dividend is 10300.

Step 8: Now we need to find the new divisor that is 23 because 463 x 23 = 10649.

Step 9: Subtracting 10649 from 10300, we get the result -349.

Step 10: Now the quotient is approximately 2.32.