How to find square root for 13 by long division method (I don't want any answer or pics or Short answer but do it step by step) please urgent
Answers
I am giving an explanation of the steps.
Take two digits at time from the decimal point to the left as well as to the right. It is possible that when you go to the left, two digits at the time you may end up with just one digit in the last group.
If there are digits after the decimal point, take two digits at a time to the right also. In this case if there is only one digit in the last group add a zero.
If the number is 77819.543
, the number would be grouped as 7¯78¯19¯.54¯30¯. In the above case since the number is 13, there is only one group i.e. 13¯.
Now find out the greatest perfect square lesser than or equal to the left most group. In case of 7¯78¯19¯.54¯30¯,
we get 22=4<7, while 32=9>7. In case of 13¯, we get 32=9<13, while 42=16>13. Write down this number (3)
above the line above the number whose square root is being calculated as well as to the left in the same line as the number whose square root is being calculated.
Now put the square of 3
below the first group and the number 3 below the 3 written earlier. Add these two 3s to get 6, which is to be written below the two 3s. Subtract the square (9) from the number in the first group (13) and write the result (4)
below.
Now bring down the number in the second group and put it next to the result of the subtraction, similar to what we do in case of ordinary division. If there are no more groups, as is in this case, put two 0
s. Now we get a three or four digit number. In case there is a decimal point before the next available group, put a decimal point on top (as we do in the case or ordinary division) while bringing down the first group after the decimal point. If the number whose square root is being determined is a whole number and there are no more groups to be brought down, put a decimal point on top (as we do in the case or ordinary division) and then put two 0
s next to the result of the subtraction.
In this case, there is only one group, so we put a decimal point after 3
on the top line and add two 0s after 4 on the last line to get 400. Note that to the left of 400 we have got a 6. Find what number can be appended to this 6 so that the resultant, when multiplied with the appended number will result in a number less than 400 while any number greater than this would result in a number greater than 400. Accordingly, we append 6. We put this number on top after the decimal point as well as to the left after 6 to get 66. We then multiply 6 and 66 to get 396, which we put below 400 and also put 6 to the left of 396 under 6. An approximate value of the square root of 13 is what we have on the top i.e. 3.6.
At the left we add 6
and 66 to get 72 and at the right we subtract 396 from 400 to get 4. Since there are no groups to be brought down and we want a greater accuracy, we add two 0s again to the result of the subtraction to get 400.
We now find that, whatever number we append to 72
and then multiply with 72, the result would be greater than 400 unless the number is 0. So we append a 0 after 72 and put a 0 after 6 on the top line. We then multiply 0 and 720 to get 0, which we put below 400 and also put 0 to the left of 400 under 0. An approximate value of the square root of 13 is what we have on the top i.e. 3.60.
At the left we add 0
and 720 to get 720 and at the right we subtract 0 from 400 to get 400. Since there are no groups to be brought down and we want a greater accuracy, we add two 0s again to the result of the subtraction to get 40000.
We now find that if we append 5
to 720 and then multiply 5 and 7205, the result would 36025 which is lesser than is 40000 whereas appending any number greater than 5 would result in a number greater than 40000. So we append a 5 after 720 and put a 5 after 0 on the top line. We then multiply 5 and 7205 to get 36025, which we put below 40000 and also put 5 to the left of 36025 under 5. An approximate value of the square root of 13 is what we have on the top i.e. 3.605.
