Square Root of 706
2026-02-28 17:41 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-706

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 706, we need to group it as 06 and 7.

Step 2: Now we need to find n whose square is ≤ 7. We can say n is ‘2’ because 2 x 2 = 4 which is less than 7. Now the quotient is 2, after subtracting 4 from 7, the remainder is 3.

Step 3: Now let us bring down 06, 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 the sum of the dividend and quotient. Now we get 4n as the new divisor, we need to find the value of n.

Step 5: The next step is finding 4n × n ≤ 306. Let us consider n as 7, now 47 x 7 = 329, which is too much, so we try n as 6.

Step 6: 46 x 6 = 276. Subtract 276 from 306, the difference is 30, and the quotient is 26.

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 3000.

Step 8: Now we need to find the new divisor that is 532 because 532 x 5 = 2660.

Step 9: Subtracting 2660 from 3000, we get the result 340.

Step 10: Now the quotient is 26.5.

Step 11: 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 √706 is approximately 26.57.