Multiplying radicals with different indexes

[ochocki]

I don't know TeX so I can't give a good example. If you have lets say a square root of m and a cube root of n, can you simply multiply them together even though the indexes are different, can someone please explain this to me?

 

[arthur ohlsten]

m^1/2 n^1/3 can't be simplified
example:
4^1/2x27^1/3
2x3
6

===========================================
m^1/2 n^1/2 = [mn]^1/2

example:
4^1/2 x 25^1/2
2x5
10

4^1/2x25^1/2
[4x25]^1/2
100^1/2
10

Arthur

 

[stapel]

I don't know TeX so I can't give a good example....

If you don't want to learn LaTeX, try instead the standard web-safe formatting explained in "Karl's Notes"? You can find a link to the article in the "Forum Help" pull-down menu at the very top of every forum page.

Eliz.

 

[Mrspi]

I don't know TeX so I can't give a good example. If you have lets say a square root of m and a cube root of n, can you simply multiply them together even though the indexes are different, can someone please explain this to me?

simplifying an expression like your example is a wonderful application of "rational eponents."

sqrt(m) can be written as m<SUP>1/2</SUP>

cuberoot(n) can be written as n<SUP>1/3</SUP>

So,

sqrt(m) * cuberoot(n) is the same thing as m<SUP>1/2</SUP>*n<SUP>1/3</SUP>

Write each of the exponents so that the denominators are the same:

m<SUP>3/6</SUP> * n<SUP>2/6</SUP>

Or,

[m<SUP>3</SUP> * n<SUP>2</SUP> ]<SUP>1/6</SUP>

Or, as a radical,

sixthroot (m<SUP>3</SUP>*n<SUP>2</SUP>)