Square Root of 697
2026-02-28 11:57 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-697

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 697, we need to group it as 97 and 6.

Step 2: Now we need to find n whose square is less than or equal to 6. We can say n is '2' because 2 x 2 = 4, which is lesser than or equal to 6. Now the quotient is 2, after subtracting 4 from 6, the remainder is 2.

Step 3: Now let us bring down 97, which makes the new dividend 297. Add the old divisor with the same number 2 + 2 to get 4, which will be our new divisor.

Step 4: The new divisor will be 4n. We need to find the value of n such that 4n x n is less than or equal to 297. Let us consider n as 6, now 46 x 6 = 276.

Step 5: Subtract 276 from 297; the difference is 21, and the quotient is 26.

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 2100.

Step 7: Now we need to find the new divisor which is 529 because 529 x 4 = 2116.

Step 8: Subtracting 2116 from 2100 is not possible, so we use 26.4 as the quotient.

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

So the square root of √697 is approximately 26.40.