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