what is the square root of 0.31428 with explanation.by divison method.
It is almost impossible to show the calculations here because the proportional font used here makes it difficult to line up calculations.
You can look up an example at the following link:
http://www.homeschoolmath.net/teaching/square-root-algorithm.php
0.560
To find the square root of 0.31428 using the division method, follow these steps:
Step 1: Arrange the given number in pairs from the decimal point. If there is an odd number of digits before the decimal point, the first pair will consist of only one digit.
In this case, the number is 0.31428. Arranging it in pairs, we have:
0.31 42 8
Step 2: Starting from the leftmost pair (0.31), find the largest digit whose square is less than or equal to the first pair (0.31). In this case, the square of 0.3 is 0.09, and it is less than 0.31. So, the largest digit is 0.3.
Step 3: Write down the digit obtained in Step 2 as the first digit of the square root. Remember the first digit is the whole number part of the square root.
So far, the square root is 0.3.
Step 4: Subtract the square of the digit obtained in Step 2 (0.3 x 0.3 = 0.09) from the first pair (0.31) to get the remainder.
0.31 - 0.09 = 0.22
Step 5: Bring down the next pair (42) after the remainder (0.22). Add a decimal point after the first digit of the square root obtained so far.
So far, the square root is 0.3 and we bring down the pair 42 after the remainder.
0.3.
Step 6: Double the current square root obtained so far (0.3) and assume a digit 'x' such that when it is placed as the next digit, the product of 'x' with the doubled square root and 'x' itself is equal to or just less than 0.42 (the next pair).
Let's assume the digit 'x' as 1. If we place 1 as the next digit and calculate (0.3 x 2 + 1) x 1, we get 0.91, which is less than 0.42.
Step 7: Write down the digit obtained in Step 6 as the next digit of the square root, to the right of the decimal point.
So far, the square root is 0.31, and we add the digit 1 obtained in Step 6.
0.31 1
Step 8: Repeat Steps 4 to 7 until all the digits have been used.
Using the same process, we get:
0.31 1 4
Total Square root: 0.31428 ≈ 0.561 (rounded to three decimal places)
Therefore, the square root of 0.31428, using the division method, is approximately 0.561.