Square Root of 800
2026-02-28 13:41 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-800

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 800, we need to group it as 00 and 8.

Step 2: Now we need to find n whose square is less than or equal to 8. We can say n as ‘2’ because 2 x 2 = 4, which is less than 8. Now the quotient is 2, and after subtracting 4 from 8, the remainder is 4.

Step 3: Now let us bring down 00, which is the new dividend, making it 400. 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, where n is a digit that when multiplied by 4n gives us a number less than or equal to 400. Let’s consider n as 7, now 47 x 7 = 329.

Step 5: Subtract 329 from 400, the difference is 71, and the quotient is 27.

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 7100.

Step 7: Now we need to find the new divisor that is 5 because 545 x 5 = 2725.

Step 8: Subtracting 2725 from 7100, we get the result 4375.

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

So the square root of √800 is approximately 28.28.