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Ac3
 one year ago
Simplify the following expression.
sqrt((1/(3(1+x)^(1/2))+(1/(3(1x)^(1/2)))
Ac3
 one year ago
Simplify the following expression. sqrt((1/(3(1+x)^(1/2))+(1/(3(1x)^(1/2)))

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freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[\sqrt{\frac{1}{3(1+x)^\frac{1}{2}}+\frac{1}{3(1x)^\frac{1}{2}}}\] is this right?

Ac3
 one year ago
Best ResponseYou've already chosen the best response.0\[\sqrt{(\frac{ 1 }{ 3(1+x)^{1/2}})^{2}+(\frac{ 1 }{ 3(1x)^{1/2} })^{2}}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[\text{ by law of exponents you can write } (\frac{1}{3(1+x)^\frac{1}{2}})^2=\frac{1^2}{3^2(1+x)^\frac{2}{2}}...\] you can do the same with the other term inside that big square root thingy

Ac3
 one year ago
Best ResponseYou've already chosen the best response.0I know how to do it. I just want to see what someone else gets.

Ac3
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ 1 }{ 3 }\sqrt{\frac{ 2 }{ 1x^2 }}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.2that is what I have too.. \[\sqrt{\frac{1}{9(1+x)}+\frac{1}{9(1x)}} \\ \sqrt{\frac{1}{9}} \sqrt{\frac{1}{1+x}+\frac{1}{1x}} \\ \frac{1}{3} \sqrt{\frac{2}{1x^2}} \]

Ac3
 one year ago
Best ResponseYou've already chosen the best response.0The reason I don't like it. Is because in these problems that I've been doing we tend to get rid of x in the expression through simplifying.

freckles
 one year ago
Best ResponseYou've already chosen the best response.2you can't get rid of x here though ...

Ac3
 one year ago
Best ResponseYou've already chosen the best response.0Since it's not disappearing makes me wonder that I did something wrong. However no matter how many times I go back I can't find anything wrong with my math.

Ac3
 one year ago
Best ResponseYou've already chosen the best response.0Take this last one for example.

Ac3
 one year ago
Best ResponseYou've already chosen the best response.0\[\sqrt{\frac{ (sinx)^2 }{ 2 }+(cosx)^2+\frac{ (sinx)^2 }{ 2 }}\]

Ac3
 one year ago
Best ResponseYou've already chosen the best response.0in that one we get rid of x. It all simplifies down to 1.

freckles
 one year ago
Best ResponseYou've already chosen the best response.2right because sin^2(x)+cos^2(x)=1 and the sqrt(1)=1

Ac3
 one year ago
Best ResponseYou've already chosen the best response.0exactly so that's why I'm a bit worried that we may be wrong. We usually tend to get rid of the x from inside of the radical at least.

freckles
 one year ago
Best ResponseYou've already chosen the best response.2if you want to rationalize the denominator you can but that would still leave x inside the radical in the numerator

Ac3
 one year ago
Best ResponseYou've already chosen the best response.0oh well, hopefully it's right. Thanks!

freckles
 one year ago
Best ResponseYou've already chosen the best response.2but the simplification you have is so far right if the problem really is: \[\sqrt{(\frac{1}{3(1+x)^\frac{1}{2}})^2+(\frac{1}{3(1x)^\frac{1}{2}})^2}\]

Ac3
 one year ago
Best ResponseYou've already chosen the best response.0yes it is. It is right. On the next part of the problem it makes sense.
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