72< x^3 < 197

Stargal411:

please help, I need it in decimal form but I cant figure it out, if u can solve it, or recommend a calculator website that can solve it in decimal form, then please do, I desperately need this.

Reply: --------

This is a range limit for the value of X (Sometimes used to limit the input or output of a function.)
The solution is

2* 3 ^(2/3) < X > 197 ^(1/3)

The numerical values are (to the 6 ^th decimal)

4.160168 > X < 5.818648


--D--

Stargal411:

please help, I need it in decimal form but I cant figure it out, if u can solve it, or recommend a calculator website that can solve it in decimal form, then please do, I desperately need this.

The opposite of cube is cube root and cube root is a power of 1/3 so

[x ³] ^1/3 = x

this works for other powers too like

[20 ⁷] ^1/7 = 20

[13 ^1/4] ⁴ = 13

[x ^1/5] ⁵ = x

Now inequalities are solved in a very similar way to equations (if you mult or divide be a neg no. you turn the sign around but that's not relevant here.)
Like with any equation, what you do to one side you must do to the other side as well, or in this case, both other sides.

72< x^3 < 19

72 ^(1/3)< [x^3] ^(1/3) < 19 ^(1/3)

And you can finish it