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First, use the identity: sqrt(x)=e^[ln(x)/2]

Then, calculate ln(x) by using the series:

2*SUM({[1/(2n+1)]*[(x-1)/(x+1)]}^(2n+1),n,0,infinity)

We'll call the above number y

Then calculate e^(y/2) via the expansion e^(y/2)=SUM{[(y/2)^n]/n!,n,0,infinity}

Since it's actually impossible to expand a number out to infinity by hand, you can almost never get the exact value of sqrt(x), but the larger the upper boundary of n you use, the more accurate the approximation.

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Q: How can you find the value of a square root number?
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What if the number is unknown to find square root square root?

It is no tpossible to find the square root of an unknown number. You can, however, represent it as x0.5 or √x so that the value of the square root can be evaluated when the value of x is known.


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The square root of a negative value is called an imaginary number.


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How to find the square root of a number?

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