What is #625^(1/4)# ?

1 Answer
Jul 12, 2017

Answer:

#625^(1/4) = 5#

Explanation:

First find the prime factorisation of #625#:

  • #625# is not divisible by #2# since it ends with an odd digit.

  • #625# is not divisible by #3# since the sum of its digits is not divisible by #3#. That is: #6+2+5 = 13# which is not divisible by #3#.

  • #625# is divisible by #5# since it ends with a #5# and we find:

#625 = 5*125 = 5*5*25 = 5*5*5*5 = 5^4#

Hence:

#625^(1/4) = (5^4)^(1/4) = 5^(4*1/4) = 5^1 = 5#