How do you simplify #root7(640 )#?

1 Answer
Dec 23, 2016

Answer:

#root(7)(640) = 2root(7)(5)#

Explanation:

There are a couple of properties that hold for any #n#th root (where #n# is a positive integer), including #7#th roots:

#root(n)(ab) = root(n)(a)root(n)(b)" "# when #a, b >= 0#

#root(n)(a^n) = a" "# when #a >= 0#

Factorising #640#, we find:

#640 = 2^7*5#

So:

#root(7)(640) = root(7)(2^7*5) = root(7)(2^7)*root(7)(5) = 2root(7)(5)#