Arithmetic and rounding

[Probability]

I can do this all day long using a calculator, but would really like to understand how it is done!

I am working with powers, I have

625 ^ 3/4 = 125

First I bring over the 4 to get;

4 square root (625)^3 = 125

OK from here the problems begin.

square root of (625) = 25, and if I square it I get back to 625, so OK with that.

But how do I work out the 4th root of the square root 625?

Once I have done that I know I will end up with 5^3 = 125

But I just don't know how to work out the 4th square root above?

 

[Deleted member 4993]

I can do this all day long using a calculator, but would really like to understand how it is done!

I am working with powers, I have

625 ^ 3/4 = 125

First I bring over the 4 to get;

4 square root (625)^3 = 125

OK from here the problems begin.

square root of (625) = 25, and if I square it I get back to 625, so OK with that.

But how do I work out the 4th root of the square root 625?

Once I have done that I know I will end up with 5^3 = 125

But I just don't know how to work out the 4th square root above?

You have not defined your problem! Is your problem:

Prove the following identity:

$\displaystyle \left [625\right ]^{\frac{3}{4}} \ = \ 125$

Or something else....

 

[serds]

625^​1/4=(625^1/2)^1/2 =

using (a^b)^c = a^b*c

 

[JeffM]

I can do this all day long using a calculator, but would really like to understand how it is done!

I am working with powers, I have

625 ^ 3/4 = 125

First I bring over the 4 to get;

4 square root (625)^3 = 125

OK from here the problems begin.

square root of (625) = 25, and if I square it I get back to 625, so OK with that.

But how do I work out the 4th root of the square root 625?

Once I have done that I know I will end up with 5^3 = 125

But I just don't know how to work out the 4th square root above?

I am not following you at all.

$\displaystyle 5^2 = 25\ and\ 625 = 25^2 \implies 625 = \left(5^2\right)^2 = 5^4$?

So $\displaystyle 625^{(3/4)} = \left(5^4\right)^{(3/4)} = 5^{(4 * 3 / 4)} = 5^3 = 125.$

 

[Probability]

I am not following you at all.

$\displaystyle 5^2 = 25\ and\ 625 = 25^2 \implies 625 = \left(5^2\right)^2 = 5^4$?

So $\displaystyle 625^{(3/4)} = \left(5^4\right)^{(3/4)} = 5^{(4 * 3 / 4)} = 5^3 = 125.$

Thanks Jeff, I've understood your method

 

[Deleted member 4993]

I can do this all day long using a calculator, but would really like to understand how it is done!

I am working with powers, I have

625 ^ 3/4 = 125

First I bring over the 4 to get;

4 square root (625)^3 = 125

How did you get to the statement above? What does "bring over the 4" mean - why would you do that?

OK from here the problems begin.

square root of (625) = 25, and if I square it I get back to 625, so OK with that.

But how do I work out the 4th root of the square root 625?

Once I have done that I know I will end up with 5^3 = 125

But I just don't know how to work out the 4th square root above?

.