What is the 4th root of 80?

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Answer 1 · 2015-09-19T22:47:03

#root(4)(80) = 2root(4)(5)#

If #a, b, c > 0# then #(ab)^c = a^cb^c#

#root(4)(x) = x^(1/4)#, so #root(4)(ab) = root(4)(a)root(4)(b)#

If #a, b, c > 0# then #(a^b)^c = a^(bc)#

So: #root(4)(a^4) = (a^4)^(1/4) = a^(4*1/4) = a^1 = a#

So:

#root(4)(80) = root(4)(2^4*5) = root(4)(2^4)root(4)(5) = 2root(4)(5)#

Answer 2 · 2015-09-19T22:53:25

#root(4)80 = 2root(4)5#

The expression #root(4)80# can be simplified if it is possible to factor out the fourth power of some integer from #80#.

Through prime factorization, we find that #root(4)80 = root(4)(2*2*2*2*5) = root(4)(2^4*5) = root(4)(2^4)root(4)(5) = 2root(4)5#