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Need help with pythagoras equations 
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#1
Nov2212, 05:56 AM

P: 2

Hi,
I need help with an explanation of how to deal with squareroots when solving equations. E.g. Look at the uploaded bmp.file and solve for x. Please I would like to have a full step by step method on how to deal with this type of equations in general. Thank you 


#2
Nov2212, 06:14 AM

HW Helper
P: 3,506

Start by squaring both sides, then show us what you've done. 


#3
Nov2212, 06:22 AM

P: 2

ok.
I managed to solve the problem so I will just ask about the squareroot. Where can I find the theory/rule of canceling squareroot? e.g. (squareroot of x)^2. 


#4
Nov2212, 08:36 AM

HW Helper
P: 3,506

Need help with pythagoras equations
If you want to read a bit more on square roots, maybe try wikipedia? Or you'll need to be more specific. 


#5
Nov2312, 08:04 AM

P: 333

When solving problems of this kind, one can square both sides and manipulate until no square roots remain. But when squaring, the implication goes only forward. Therefore, one must check all solutions one finds by inserting them into the original equation.
For example, squaring the equation ##\sqrt x =1## gives ##x=1##. The first equation can therefore have no solution other than ##x=1##. But if we insert this in the first eqaution, we obtain ##\sqrt 1=1##, which is false. Therefore, ##x=1## is not a solution either, so the first equation has no solutions. 


#6
Nov2312, 08:11 AM

P: 295

[itex]\sqrt[n]{x}[/itex]'s principal branch value is defined so as to be the unique real number a satisfying [itex]a\in\sqrt[n_m]{x}[/itex] and [itex]a\geq 0[/itex], where [itex]\sqrt[n_m]{}[/itex] denotes the multivalued version of the nth root. I just wanted to point that out to avoid confusion. 


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