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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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Related questions

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.


Does the square root of 2 or 1.5 have the greater value?

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.


The square root of a negative value is called an or complex number?

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


How do you determine the value of the number if you already have your square root?

To get the original number, multiply the square root of the number by itself.


How do you find the value number if you already have a square root?

Multiply the square root by itself. After you do that, please discuss the idea of square roots with somebody who knows. You don't understand them yet.


How do find the sqaure root of a number?

To find the square root of a number you multiply that number by it self twice.(example) the square root of 9 ? the square root of nine is 81 as 9X9=81. square root of 4 ? th square root of is 16 as 4X4=16.


What is the absolute value of a complex number?

The absolute value of a complex number a+bi is the square root of (a2+b2). For example, the absolute value of 4+9i is the square root of (42 + 92) which is the square root of 97 which is about 9.8489 (The absolute value of a complex number is not complex.)


How do you find out if a number is a square?

square root it


How to find the square root of a number?

to find the square root of a number you need to find the number that multiplied by its self is that number example: the square root on 9 is 3 it is 3 because 3 x 3 - 9


Square root of a value?

The square root of a value v is a number x such that, x multiplied by x equals v. Note that -x is also a square root.


How to find square root of a number?

Press the square root button on your calculator.


What does x value in square root mean?

It is the number whose square root you need to obtain.