# Algebra

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True or False.
The fifth root of a positive integer is sometimes irrational. Please give an example or a counterexample so that I can understand it fully.

• Algebra -

There is no counterexample. The fifth root is indeed sometimes irrational.

Pick any integer which is not a perfect 5th power, and its 5th root is irrational.

5th powers: 0,1,32,343,1024,3125,...
These all have rational 5th roots: 0,1,2,3,4,5,...

Any numbers in between those have irrational 5th roots.

Not only is the 5th root sometimes irrational, it is "almost always" irrational. And yet, infinity is a strange animal. While it seems like the vast majority of integers ought to have irrational 5th roots, there are just as many which have rational 5th roots.

• Algebra -

find the value of 7+2(5-2.3^2).

• Algebra -

why? Have you no calculator?

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