Square Root of 608
2026-02-28 12:59 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-608

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 608, we need to group it as 08 and 6.

Step 2: Now we need to find n whose square is ≤ 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, and after subtracting 4 from 6, the remainder is 2.

Step 3: Now let us bring down 08, 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 x n ≤ 208. Let us consider n as 5, now 45 x 5 = 225, which is more than 208, so we consider n as 4.

Step 6: 44 x 4 = 176. Subtracting 176 from 208, the difference is 32, and the quotient is 24.

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 3200.

Step 8: Now we need to find the new divisor, which is 4n. Let's assume n as 6, 496 x 6 = 2976.

Step 9: Subtracting 2976 from 3200, we get the result 224.

Step 10: Now the quotient is 24.6

Step 11: 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 √608 is approximately 24.66.