Square Root of 105.79
2026-02-28 12:42 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-105.79

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 of 105.79 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 105.79, we need to group it as 05, 10, and .79.

Step 2: Now we need to find n whose square is less than or equal to 10. We can say n is '3' because 3^2 = 9 is less than 10. Now the quotient is 3, after subtracting 9 from 10, the remainder is 1.

Step 3: Now let us bring down 05, which is the new dividend. Add the old divisor with the same number, 3 + 3, to get 6, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 6n as the new divisor; we need to find the value of n.

Step 5: The next step is finding 6n × n ≤ 105. Let us consider n as 1, now 6 × 1 × 1 = 6.

Step 6: Subtract 105 from 6, the difference is 99, and the quotient is 10

Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to bring down 79. Now the new dividend is 979.

Step 8: Now we need to find the new divisor that is 206 because 206 × 4 = 824.

Step 9: Subtracting 824 from 979, we get the result 155.

Step 10: Now the quotient is 10.2.

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose there are no decimal values; continue till the remainder is zero.

So the square root of √105.79 is approximately 10.29.