Square Root of 5450
2026-02-28 15:55 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-5450

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 5450, we need to group it as 50 and 54.

Step 2: Now we need to find n whose square is 54. We can say n is ‘7’ because 7 x 7 = 49, which is lesser than or equal to 54. Now the quotient is 7, after subtracting 54 - 49, the remainder is 5.

Step 3: Now let us bring down 50, forming the new dividend of 550. Add the old divisor with the same number: 7 + 7 = 14, which will be our new divisor.

Step 4: The new divisor will have a tenths digit to form 14n. We need to find a digit for n so that 14n x n is less than or equal to 550. Let us consider n as 3, now 143 x 3 = 429.

Step 5: Subtract 429 from 550, the difference is 121, and the quotient is 73.

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 12100.

Step 7: Now we need to find the new divisor, which is 147, because 1473 x 3 = 4419.

Step 8: Subtracting 4419 from 12100, we get the result 7681.

Step 9: Continue doing these steps until you get two numbers after the decimal point. If there is no decimal value, continue till the remainder is zero.

So the square root of √5450 ≈ 73.793