Square Root of 715
2026-02-28 19:06 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-715

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 715, we need to group it as 15 and 7.

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

Step 3: Bring down 15, 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 previous divisor and the quotient. Now we get 4n as the new divisor, and we need to find the value of n.

Step 5: The next step is finding 4n × n ≤ 315. Let us consider n as 7, now 47 × 7 = 329, which is greater than 315. So, we try n as 6: 46 × 6 = 276.

Step 6: Subtract 276 from 315, the difference is 39, and the quotient is 26.

Step 7: Since the new 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 3900.

Step 8: The new divisor is 532 because 532 × 7 = 3724, which is less than 3900.

Step 9: Subtracting 3724 from 3900, we get the remainder 176.

Step 10: Now the quotient is 26.7

Step 11: Continue doing these steps until we get two numbers after the decimal point or until the remainder is zero.

So the square root of √715 is approximately 26.73.