7 replies to this topic

[James Noel]

Hi, can anyone tell me how to evaluate (sqr(x) * sqr(x^3))/x^-3. I know I am suppose to get x^5 but the classpad manager is giving other wise. Can some one please help. Thanks in adance.

[McCoy]

Hi, can anyone tell me how to evaluate (sqr(x) * sqr(x^3))/x^-3. I know I am suppose to get x^5 but the classpad manager is giving other wise. Can some one please help. Thanks in adance.

I don't want to cut you down mate, but I have to say something for your benefit: "don't" ever use a calculator for such expressions.
Use your pen and a paper. It gives you an idea of what you are doing and the skill you gained in manipulating equations will help you if you happen to pursue a career in physical scineces(Chemistry or physics) or mathematics. A calculator doesn't tell you what it's doing or worse, it can't always do what you want it to do.

(a) pen and a paper: note square root is the same as raising a number to a power of two; so x^(1/2)*x^(3*1/2)/x^-3 = x^(1/2) * x^(3/2)*x^3 = x^(4/2)*x^3 = x^2 *x^3 = x^5.
or sqrt(x)*sqrt(x^3)/x^-3 = sqrt(x*x^3)/x^-3 = sqrt(x^4)/x^-3 = x^2/x^-3 = x^2*x^3 = x^5.
(b)use a calculator but you need to simpilify the result using pen and paper to the form you want!

[supergems]

Simplification of radicals depends on the calculator's CAS. With the HP 50g,

with "Rigorous" option on: '\v/X*(\v/(X^3)/X^-3)' EVAL --> 'X^4*ABS(X)' ('\v/'=SQRT)
with "Rigorous" option off: '\v/X*(\v/(X^3)/X^-3)' EVAL --> 'X^5'


P.S. "Rigorous" option is in MODE-->CAS.

[ASTRO491K]

You don't say what answer you are getting but I suspect that the answer you got doesn't combine the sqrt(x)*sqrt(x^3). For example you might get x^(7/2)*sqrt(x^3),

Hi, can anyone tell me how to evaluate (sqr(x) * sqr(x^3))/x^-3. I know I am suppose to get x^5 but the classpad manager is giving other wise. Can some one please help. Thanks in adance.

[ASTRO491K]

Sorry, I pressed the wrong button. The point I was about to make is that for positive numbers, sqrt(x)*sqrt(x^3) produces the same answer as sqrt(x^4)=x^2. Try the number one for instance. One squared is one. However for negative values of x that is not true. Try minus one for instance. Minus one squared is plus one but the sqrt(-1) is i and the sqrt((-1)^3) is i and i times i is minus one not plus one. So the simplification doesn't work for negative numbers in which case x^5 is not the correct answer for negative values of x. P.S. You have to have a little experience with complex numbers to understand what I have said, or you must simply take it on faith.

You don't say what answer you are getting but I suspect that the answer you got doesn't combine the sqrt(x)*sqrt(x^3). For example you might get x^(7/2)*sqrt(x^3),

[supergems]

I agree with you, in this case the ClassPad performs better because it returns a simplification (x^(7/2)*sqrt(x^3)) that takes into account that x must be greater than or equal to 0....

[ASTRO491K]

Thank you. The problem is that many high school teachers don't know enough about math to teach students that
sqrt(s)*sqrt(=sqrt(a* applies to positive values only.

[quote name='supergems' post='48650' date='Feb 16 2010, 10:09 AM']I agree with you, in this case the ClassPad performs better because it returns a simplification (x^(7/2)*sqrt(x^3)) that takes into account that x must be greater than or equal to 0....[/quote]

Thank you. The problem is that many high school teachers don't know enough about math to teach students that
I mean sqrt(a)*sqrt(=sqrt(a* applies to positive values only.

I don't know what is going on but smiley faces are being inserted where I did not insert them! Strange, very strange.

[quote name='ASTRO491K' date='Feb 17 2010, 09:56 AM' post='48656']
Thank you. The problem is that many high school teachers don't know enough about math to teach students that
sqrt(s)*sqrt( =sqrt(a* applies to positive values only.