sqrt issue
- Thread starter bcddd214
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Hello, bcddd214!
Are you trying for a new world record?
Let's look at what you've done . . .
\(\displaystyle \sqrt{1 + \frac{2}{y^6}} \;=\;\sqrt{1} + \sqrt{\frac{2}{y^6}}\) .?
. . . . . . . \(\displaystyle =\;1 + \frac{\sqrt{2}}{\sqrt{y^6}}\)
Now: .\(\displaystyle \sqrt{2} \,=\,4\) .?
and: .\(\displaystyle \sqrt[2]{y^6} \:=\:y^{6-2} \:=\:y^4\) .?
\(\displaystyle \text{So you have: }\:1 + \frac{4}{y^4}\)
Was that your reasoning?
Are you trying for a new world record?
Let's look at what you've done . . .
\(\displaystyle \sqrt{1 + \frac{2}{y^6}} \;=\;\sqrt{1} + \sqrt{\frac{2}{y^6}}\) .?
. . . . . . . \(\displaystyle =\;1 + \frac{\sqrt{2}}{\sqrt{y^6}}\)
Now: .\(\displaystyle \sqrt{2} \,=\,4\) .?
and: .\(\displaystyle \sqrt[2]{y^6} \:=\:y^{6-2} \:=\:y^4\) .?
\(\displaystyle \text{So you have: }\:1 + \frac{4}{y^4}\)
Was that your reasoning?
D
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bcddd214 said:
Without knowing exactly where did "that" come from - I have to say it cannot be reduced further.
J
JeffM
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No.bcddd214 said:
mmm4444bot
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JeffM said:
mmm4444bot
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bcddd214 said:
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.
Re:
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!
mmm4444bot said:
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!
J
JeffM
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Re:
mmm4444bot said:
JeffM said:No.bcddd214 said:
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])
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
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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
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bcddd214 said: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.
J
JeffM
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Re:
You got me right between the eyes.mmm4444bot said: