sqrt issue

[bcddd214]

Brain fart,,,

doesn't ?(1+2/y^6) evaluate to 1+4/y^4?

[soroban]

Hello, bcddd214!


\text{Doesn't }\sqrt{1+\frac{2}{y^6}}\,\text{ evaluate to: }\,1 +\frac{4}{y^4}\:?
Are you trying for a new world record?


Let's look at what you've done . . .

\sqrt{1 + \frac{2}{y^6}} \;=\;\sqrt{1} + \sqrt{\frac{2}{y^6}} .?

. . . . . . . =\;1 + \frac{\sqrt{2}}{\sqrt{y^6}}


Now: .\sqrt{2} \,=\,4 .?

and: .\sqrt[2]{y^6} \:=\:y^{6-2} \:=\:y^4 .?

\text{So you have: }\:1 + \frac{4}{y^4}


Was that your reasoning?

[Subhotosh Khan]

Brain fart,,,

doesn't ?(1+2/y^6) evaluate to 1+4/y^4? No



Without knowing exactly where did "that" come from - I have to say it cannot be reduced further.

[Denis]

Brain fart,,,
doesn't ?(1+2/y^6) evaluate to 1+4/y^4?
Next time, check these silly things yourself:
assign a value to y, then CHECK!
Say we use y=1:
sqrt(1 + 2/y^6) = sqrt(3)
1 + 4/y^4 = 5
Does sqrt(3) = 5 ?

[bcddd214]

I apologize
doesn't ?(1+(4/y^6)) evaluate to 1+2/y^4?.

[JeffM]

I apologize
doesn't ?(1+(4/y^6)) evaluate to 1+2/y^4?.
No.

[mmm4444bot]

doesn't ?(1+(4/y^6)) evaluate to 1+2/y^4?


No.

Actually, the correct answer to bcddd214's question above is "yes". :lol:

[mmm4444bot]

doesn't ?(1+ 4/y^6) evaluate to 1 + 2/y^4?

Please note that I removed the unneccesary grouping symbols from the first expression above.



We cannot evaluate sqrt(1 + 4/y^6) without knowing the value of y. I think that you're trying to ask about simplifying, instead.

So, yes, the expression sqrt(1 + 4/y^6) does not simplify to 1 + 2/y^4.

[bcddd214]

doesn't ?(1+ 4/y^6) evaluate to 1 + 2/y^4?

Please note that I removed the unneccesary grouping symbols from the first expression above.



We cannot evaluate sqrt(1 + 4/y^6) without knowing the value of y. I think that you're trying to ask about simplifying, instead.

So, yes, the expression sqrt(1 + 4/y^6) does not simplify to 1 + 2/y^4.



Thank you.
The reason I 'thought' it did was because it looked pretty BUT, Maple said the same thing as you.
I plugged in evalf (sqrt(1+(4/y^6))); and it spit out the identical equation hinting that it could not be done.
I was just double checking the calculators answer to confirm there was no user error.
Thank you!

[JeffM]

doesn't ?(1+(4/y^6)) evaluate to 1+2/y^4?


No.

Actually, the correct answer to bcddd214's question above is "yes". :lol:
You are the mathematician, but may a wannabe historian present a possible counter-example a la mode du bon Denis.
Let's try y = 2.
(1 + (4/y[sup:3ud5rmel]6[/sup:3ud5rmel]))[sup:3ud5rmel]1/2[/sup:3ud5rmel] = (1 + (4/2[sup:3ud5rmel]6[/sup:3ud5rmel]))[sup:3ud5rmel]1/2[/sup:3ud5rmel] = (1 + (4/64))[sup:3ud5rmel]1/2[/sup:3ud5rmel] = (1 + (1/16))[sup:3ud5rmel]1/2[/sup:3ud5rmel] = sqrt(17) / 4.
1 + (2/y[sup:3ud5rmel]4[/sup:3ud5rmel]) = 1 + (2/16) = 1 + (1/8) = 9/8.
But (9/8)[sup:3ud5rmel]2[/sup:3ud5rmel] = 81/64 = 5.0625/4.
My problem is seeing how 5.06252[sup:3ud5rmel]2[/sup:3ud5rmel] > 25 = 17.
Of course, I admittedly am frequently in error, and arithmetic is not my forte, but I would love to know how you demonstrate that (1 + (4/y^6))[sup:3ud5rmel]1/2[/sup:3ud5rmel] = 1 + (2/y[sup:3ud5rmel]4[/sup:3ud5rmel]) :P

PS I have this horrible feeling I am going to look extremely foolish before this is all over. Such as, you were teasing me and I was too literal-minded to twig, or else that devil Alzheimers has indeed caught up with me (which my newly acquired 18-year old wife keeps assuring me is the case as she hands me the power of attorney papers to sign).

[mmm4444bot]

Yeah, I was joshin' Jeff.

bcddd214 did not ask, "Does [this] evaluate to [that]".

They asked, "Does not [this] evaluate to [that]".

It does not, so the answer is "yes".

(I hope you're smiling right now.)

[mmm4444bot]

The reason I 'thought' it did was because it looked pretty

Just as in life, looks can be deceiving. Don't be fooled by every pretty expression that crosses your path.


I plugged in evalf(sqrt(1+(4/y^6))); and it spit out the identical equation hinting that it could not be done.

That's because EVALF() is Maple's command for "evaluate the expression to a floating point number". You cannot get a Real number for this expression without first knowing a number that symbol y represents.

If you do not have any values for the symbol y, then the expression remains symbolic.

Another note about terminology: we don't call sqrt(1 + 4/y^6) an equation; it's called an expression. Equations always contain an equals sign. 8-)

[JeffM]

Yeah, I was joshin' Jeff.

bcddd214 did not ask, "Does [this] evaluate to [that]".

They asked, "Does not [this] evaluate to [that]".

It does not, so the answer is "yes".

(I hope you're smiling right now.)


You got me right between the eyes.

[Denis]

You got me right between the eyes.
...you asked for it: you were leading with your nose 8-)