how do we find the square root of a number?!?!?
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We can take out the square of any number by the long division method. Let's take an easy example first, say 8100. We already know it's square root; i.e. 90. By the long division, we can obtain it as follows→
Write the number and make groups of two. ( Start from right side)
Now, we get 2 groups, i.e. 81 00
Now, think of least number, by which we can get 81. ( In this case, it is a perfect square but we can take any no. just like division, then we'll take the no. which is less than it.)
So we write 9*9 ( Note- In division we can take any multiples like 9*4, 9*3 etc. but in the case finding square roots, we consider only squares. So we'll write 9*9.)
Now, we add quotient i.e. 9+9 which is 18.Clearly, 180*0 is 0*0=0, thus, 90 is the square root of 8100.
Now let's take a bite harder no., 5859.
Make the groups i.e. 58 59 ( from right side)
Now, closest square is 7*7=49
Subtracting 49 from 58=9
Bring down 59 ( We bring the whole group down)
Adding the quotient, we get 7+7=14.
Now, closest no. to 959 is 146*6 which is 876.
Remaider=8
Adding the quotient we get, 14+6=20
Bring 2 zeroes down( We'll do like decimal now)
Therefore, closest square is now 205*5=1025
Hence, the answer is 76.5
(Note- Here we've taken it to only 1 decimal place. we can continue like this forever :P)
Hope it helped. I know it has got complicated because I don't know how to use a flowchart here.
Write the number and make groups of two. ( Start from right side)
Now, we get 2 groups, i.e. 81 00
Now, think of least number, by which we can get 81. ( In this case, it is a perfect square but we can take any no. just like division, then we'll take the no. which is less than it.)
So we write 9*9 ( Note- In division we can take any multiples like 9*4, 9*3 etc. but in the case finding square roots, we consider only squares. So we'll write 9*9.)
Now, we add quotient i.e. 9+9 which is 18.Clearly, 180*0 is 0*0=0, thus, 90 is the square root of 8100.
Now let's take a bite harder no., 5859.
Make the groups i.e. 58 59 ( from right side)
Now, closest square is 7*7=49
Subtracting 49 from 58=9
Bring down 59 ( We bring the whole group down)
Adding the quotient, we get 7+7=14.
Now, closest no. to 959 is 146*6 which is 876.
Remaider=8
Adding the quotient we get, 14+6=20
Bring 2 zeroes down( We'll do like decimal now)
Therefore, closest square is now 205*5=1025
Hence, the answer is 76.5
(Note- Here we've taken it to only 1 decimal place. we can continue like this forever :P)
Hope it helped. I know it has got complicated because I don't know how to use a flowchart here.
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