Square Root of 5392
2026-02-28 15:48 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-5392

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 5392, we need to group it as 92 and 53.

Step 2: Now we need to find n whose square is less than or equal to 53. We can say n as ‘7’ because 7 x 7 = 49, which is lesser than or equal to 53. Now the quotient is 7 after subtracting 53 - 49, the remainder is 4.

Step 3: Now let us bring down 92, which is the new dividend. Add the old divisor (7) with itself, we get 14, which will be our new divisor.

Step 4: The new divisor will be 14n. We need to find the value of n.

Step 5: The next step is finding 14n × n ≤ 492. Let us consider n as 3, now 14 x 3 = 42, so 423 x 3 = 1269, which is less than or equal to 492.

Step 6: Subtract 492 from 423, the difference is 69.

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 6900.

Step 8: Now we need to find the new divisor. It turns out to be 147, because 1473 x 3 = 4419.

Step 9: Subtracting 4419 from 6900, we get the result 2481.

Step 10: Now the quotient is 73.4.

Step 11: Continue doing these steps until you get two numbers after the decimal point. Suppose there is no decimal value, continue until the remainder is zero.

So, the square root of √5392 is approximately 73.41.