2/3 root of a number

[anmldr]

Is the 2/3 root of a number i.e. number^2/3 the same as number^.6667 ?

Or, is the number squared and then the cubed root taken of that number...or are they the same?

Linda

 

[Deleted member 4993]

Is the 2/3 root of a number i.e. number^2/3 the same as number^.6667 ?

Or, is

the number squared and then the cubed root taken of that number << This is most preferable.


...or are they the same? << They are almost same - not quite. Try with 64 - the answer should be 16 but if use 0.667 you'll get16.00222

Linda

 

[soroban]

Hello, Linda!

Did you mean to use the word "root"?

Is the 2/3 root of a number i.e. number^2/3 the same as number^.6667 ?

Or is the number squared and then the cubed root taken of that number . . . or are they the same?

\(\displaystyle \text{Are you talking about a }power\text{ of a number?}\)

\(\displaystyle \text{The }\tfrac{2}{3}\ower\text{ of }x\text{ is: }\:x^{\frac{2}{3}}\)


Note that, with roots, we use reciprocals.

. . \(\displaystyle \text{The }4^{th}\text{ root of }x\text{ is: }\:x^{\frac{1}{4}\)

. . \(\displaystyle \text{The }6^{th}\text{ root of }y\text{ is: }\:y^{\frac{1}{6}}\)

\(\displaystyle \text{Hence, the }\tfrac{2}{3}\text{ root of }x\text{ is: }\:x^{\frac{3}{2}}\)

 

[Deleted member 4993]

Soroban is absolutely correct. I missed the designation "root"..... Oh well ....now Dennis will make fun of me again....

 

[Denis]

Oh well ....now Dennis will make fun of me again....

No, I won't, because I didn't see that terrible unforgivable error of yours :shock:

 

[chrisr]

i.e. number^2/3

redemption