Square Root of 473
2026-02-28 08:44 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-473

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 473, we group it as 73 and 4.

Step 2: Now we need to find n whose square is less than or equal to 4. We can say n is ‘2’ because 2 x 2 = 4. Now the quotient is 2, and after subtracting 4 - 4, the remainder is 0.

Step 3: Now let us bring down 73, which is the new dividend. Add the old divisor with the same number 2 + 2 we get 4, which will be our new divisor.

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

Step 5: The next step is finding 4n × n ≤ 73. Let us consider n as 1, now 41 x 1 = 41.

Step 6: Subtract 73 from 41; the difference is 32, and the quotient is now 21.

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 zeros to the dividend. Now the new dividend is 3200.

Step 8: Now we need to find the new divisor. Let n be 7 because 437 x 7 = 3059.

Step 9: Subtracting 3059 from 3200, we get the result 141.

Step 10: Now the quotient is 21.7

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

So the square root of √473 is approximately 21.72.