what is square root of 0.31428 from divison method.
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square root of 0.31428 from divison method
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To find the square root of 0.31428 using the division method, you can follow these steps:
Step 1: Start by setting up the problem as a division. Place a square root symbol (√) above the dividend (0.31428) and a blank line under the dividend.
√0.31428
_______
Step 2: Divide the dividend into pairs of numbers, starting from the decimal point. In this case, we have 31, 42, and 8. Add a decimal point above and below the line.
√0.31428
_______
31
Step 3: Find the largest perfect square that is less than or equal to the first pair of numbers (31). In this case, the largest perfect square is 25. Write it below the line, next to the dividend.
√0.31428
_______
31
25
Step 4: Divide the number below the line (25) by the divisor (the number you just placed on the line). Write the quotient above the line and the remainder below the line.
√0.31428
_______
31
25
--
6
Step 5: Bring down the next pair of numbers (42) to the right of the remainder and place them next to it.
√0.31428
_______
31
25
--
64
Step 6: Double the quotient you obtained earlier (in this case, it's 3) and write it at the right of the existing quotient. Place a blank on top of this new number.
√0.31428
_______
31
25
-3--
64
Step 7: Guess a digit to be placed on the blank in a way that the product of the new divisor and the new number (6X) is less than or equal to the dividend. In this case, when we try with 61, it results in a product (61 x 61) of 3721, which is greater than 314. Therefore, we have to use 60 as our new number and write it in place of the blank. Multiply the new divisor (60) by the new number (6) and subtract it from the numbers below the line.
√0.31428
_______
31
25
-3--60
64
-60
--
44
Step 8: Bring down the next pair of numbers (84) to the right of the remainder and place them next to it.
√0.31428
_______
31
25
-3--60
64
-60
--
448
Step 9: Repeat steps 6-8 until you have enough decimal places or reach a desired level of accuracy. Continuing from the previous step:
√0.31428
_______
31
25
-3--60
64
-60
--
448
-448
----
0
Step 10: Once you reach zero or have obtained the desired level of accuracy, the numbers above the line will be the square root of 0.31428 from the division method.
In this case, the square root of 0.31428 from the division method is approximately 0.5601.