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# Find the square root of 125 by long division method.

Last updated date: 20th Jun 2024
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Hint: We will first select 1 as the number and then multiply it with such number so that (10 + x)x is less than or equal to 25 and thus, we have the square root.

Now, we have 125 with us whose square root we require to find.
We can write 125 as 1,25 for our understanding.
So, the first digit will be 1 whose square is 1 and will be less than or equal to 1.

Like in the above picture, we took 1, multiplied it by 1 and then after its cancellation and all, we got 25 as the term for next division.
Now, we will write 2 as the divisor, 25 as dividend and we will have to find a digit x such that (20 + x) x is maximum but still less than 25. That digit would be definitely 1, because 21 (1) < 25 < 22 (2).
So, we get with us the following picture:-

Now, we get 4 as the next dividend and the divisor will be 22. Therefore, we will have to get the zeroes from above after decimal twice and then find such a y that (220 + y) y is less than 400. That digit is but obviously 1 and thus we get the following picture as the next step:

After the division, as we see above, we have got 179 as dividend and thus 222 as the divisor. So, we will have to get two zeroes from above.
We now have to find such a z such that (2220 + z) z is maximum but still less than or equal to 17900. And, if we keep on going like this, we will get the following division:-

Hence, the square root of 125 is 11.1803…

Note:
The students must note that in the long division method as done above, we try to get 0 as the dividend for the next step so as we have a definite square root.
The students must also note that: we always get the divisor of the next step by multiplying the quotient by 2 and that will be the divisor we use in the next step.
The students should also know that after getting the divisor we have to put such a digit as the end so that if we multiply the whole new divisor we got after putting that digit, with that digit only, we get the maximum product which is still less than the dividend we use in that step.