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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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Since the square root of a number is the "number times itself that equals the original number," it makes sense that the larger the original number, then the larger the square root. The value of the square root of 2 will be greater than the value of the square root of 1.5.


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The square root of 7400 is 86.0232526704. To find the square root of a number, you can use a calculator or a mathematical formula. The square root of a number is a value that, when multiplied by itself, gives the original number.


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


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The square root of 225 is 15. This is because the square root of a number is a value that, when multiplied by itself, gives the original number. In this case, 15 multiplied by 15 equals 225. Therefore, the square root of 225 is 15.


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