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Question 573141: What is the square root of 1700? This is what I have so far:
1700 412
-16
--
81 100
81
----
82 1900
Now we are lost. I am a homeschool mom trying to help my son understand this.
I have the answer, but not how to get the answer, so if you could include the math for each step I would appreciate it. Thank you for your help
Found 2 solutions by scott8148, solver91311:
Answer by scott8148(6628)   (Show Source):
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website!
Starting at the decimal point and moving left, group your digits into pairs leaving a single digit as a lead digit if there are an odd number of digits to the left of the decimal point. If your radicand (the number under the radical) has decimal places, add a zero to make it an even number of digits and then add pairs of zeros until the number of digit pairs to the right of the decimal point is equal to the number of decimal places of accuracy that you want for your answer.
Examine the leftmost grouping of digits in your radicand. Select the largest number that when squared is less than or equal to the leftmost digit(s). In your case, your leftmost digits are 17, so since 4 X 4 = 16 which is less than 17 and 5 times 5 is 25 which is more than 17, select 4 as your initial divisor. 4 goes into 17 4 times, so put a 4 above the 7 outside of the radical sign.
Just like in long division, multiply your partial quotient by the divisor 4 X 4 = 16. Put the 16 below the 17 and subtract, leaving 1.
Bring down the next two digits, 00 in your case, giving us a new partial radicand of 100.
The new divisor will be a two-digit number where the 10s digit is two times the current partial quotient (2 times 4 = 8) and the 1s digit is selected so that the ones digit when multiplied by the new divisor will be less than or equal to the partial quotient. Here, you have 80 + some units digit. If the units digit is 1 then 1 times 81 is 81 and that is less than 100. But if the units digit were 2, then 2 times 82 is 164 which is too large. Hence the units digit for this divisor and the next digit in the quotient must be 1. Put the 1 above the second zero to the right of the 7 in your radicand and 81 in line with and to the left of your 100 partial radicand.
Now, 1 times 81 is 81 and you put the 81 below the 100. Subtract to get 19. Bring down the next pair of digits from your radicand. In your problem this is the first pair of zeros you added to the right of the decimal point.
New partial radicand is 1900.
New divisor 2 times the entire partial quotient plus some units digit. 2 times 41 is 82, so your new divisor is 820 plus some units digit.
If the units digit were 1, then you would have 1 times 811 equals 811, certainly less than 1900, but is that the best we can do? If the units digit is 2, then we have 2 times 822 equals 1644 -- ah ha! still less than 1900. But if the units digit is 3, we have 3 times 823 equals 2469; way too much. 2 is the answer. 2 goes above the second zero to the right of the decimal point, 822 to the left of the 1900, 1644 below the 1900.
Subtract
New partial quotient 41.2
New partial radicand 35600
New divisor 8240 plus some units digit -- looks like a 4 will work...
And so on. Continue the pattern for as many decimal point accuracy as you like. But don't expect the result of any subtraction step to ever be zero unless you started with a perfect square radicand in the first place.  is an irrational number, hence the decimal representation goes on forever never repeating any pattern of digits.
John
My calculator said it, I believe it, that settles it
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