The cube root.. need HELP solving cbrt(50 - 19 sqrt(7))

[4str0]

Hello everyone!
I'm sorry if i writing in wrong topic. I have the following problem to solve:

. . . . .\(\displaystyle \sqrt[3]{\strut 50\, -\, 19\, \sqrt{\strut 7\,}\,}\)

I tried to square or cube but nothing..
honestly now i have no idea how to solve this. Would be grateful for any help! Thank you.

 

[Deleted member 4993]

Hello everyone!
I'm sorry if i writing in wrong topic. I have the following problem to solve:

. . . . .\(\displaystyle \sqrt[3]{\strut 50\, -\, 19\, \sqrt{\strut 7\,}\,}\)

I tried to square or cube but nothing..
honestly now i have no idea how to solve this. Would be grateful for any help! Thank you.

In the absence of any restrictions - why not simply put it in the calculator and calculate?

. . . . .\(\displaystyle \sqrt[3]{\strut 50\, -\, 19\, \sqrt{\strut 7\,}\,}\, \approx\, -0.64575\)

 

[stapel]

I have the following problem to solve:

. . . . .\(\displaystyle \sqrt[3]{\strut 50\, -\, 19\, \sqrt{\strut 7\,}\,}\)

This is just an expression. It can be simplified or rearranged or evaluated, but it cannot be solved. Only "equations" (things with "equals" signs and a variable) can be solved. So what is the full and exact text of the exercise (for instance, is there an "equals" and another side to this) and what were the complete instructions (for instance, did they really say to "solve")?

I tried to square or cube but nothing..

When you reply, please include a clear listing of your efforts so far. Thank you!

 

[4str0]

This is just an expression. It can be simplified or rearranged or evaluated, but it cannot be solved. Only "equations" (things with "equals" signs and a variable) can be solved. So what is the full and exact text of the exercise (for instance, is there an "equals" and another side to this) and what were the complete instructions (for instance, did they really say to "solve")?[/COLOR]


When you reply, please include a clear listing of your efforts so far. Thank you!

Sorry, my bad.
Author ask to calculate it but i think it should be simplified to more simple expression like 2sqrt(17) or something similar.

 

[stapel]

Author ask to calculate it but i think it should be simplified to more simple expression like 2sqrt(17) or something similar.

If you're supposed to calculate it (that is, to find the decimal approximation), then just go do that. Plug it into your calculator, and copy down whatever digits you get.

 

[4str0]

If you're supposed to calculate it (that is, to find the decimal approximation), then just go do that. Plug it into your calculator, and copy down whatever digits you get.

Haha. Yeah it would be great until i'll show this to my teacher. It should be done without calculator. alright i got it. And what about simplifying? Do you have any idea?

 

[Deleted member 4993]

Haha. Yeah it would be great until i'll show this to my teacher. It should be done without calculator. alright i got it. And what about simplifying? Do you have any idea?

Do you know the procedure for solving a sixth order polynomial?

 

[4str0]

Do you know the procedure for solving a sixth order polynomial?

Thanks a lot . I think i found it. )
The answer is 3. or sqrt(729)^6

 

[lookagain]

Hello everyone!
I'm sorry if i writing in wrong topic. I have the following problem to solve:

. . . . .\(\displaystyle \sqrt[3]{\strut 50\, -\, 19\, \sqrt{\strut 7\,}\,}\)

I tried to square or cube but nothing..
honestly now i have no idea how to solve this. Would be grateful for any help! Thank you.

You should find out if the expression is to be rewritten in the form \(\displaystyle \ \ a + b\sqrt{7} \ \ for \ \ the \ \ answer, \ \ \) where a and b are integers.

\(\displaystyle (a + b\sqrt{7})^3 \ = \)


\(\displaystyle a^3 + 3a^2b\sqrt{7} + 3a(b\sqrt{7})^2 + (b\sqrt{7})^3 \ = \ \)


\(\displaystyle a^3 + 3a^2b\sqrt{7} + 21ab^2 + 7b^3\sqrt{7} \)



Equate corresponding parts:


\(\displaystyle a^3 + 21ab^2 \ = \ 50 \)


\(\displaystyle 3a^2b\sqrt{7} + 7b^3\sqrt{7} \ = \ -19\sqrt{7} \)
------------------------------------



Divide both sides of the second equation by \(\displaystyle \ \ \sqrt{7}.\)



\(\displaystyle a^3 + 21ab^2 \ = \ 50 \)


\(\displaystyle 3a^2b + 7b^3 \ = \ -19 \)
------------------------



Then you would look for some further strategy...

 

[Steven G]

Thanks a lot . I think i found it. )
The answer is 3. or sqrt(729)^6

No, the answer is not 3, the answer is a negative number. Also, sqrt(729)^6 \(\displaystyle \ne\) 3 or do you think that there are two answers, 3 and sqrt(729)^6??

In the end you WILL need to use a calculator so why bother trying to simplify it before using a calculator????