Find an irrational number that is between 5.2 and 5.5. explain why it is irrational. include the decimal approximation of the irrational number to the nearest hundredth.

Hello,

5.2²=27.04
5.5²=30.25

So
5.2<√28<5.5    √28≈5,29
or
5.2<√29<5.5    √29≈5,39
or
5.2<√30<5.5    √30≈5,48

But we may also use ∛

5.2³=140,608
5.5³=166,375

So
5.2<∛141<5.5 and ∛141=5,20482≈5.20
5.2<∛142<5.5 and ∛142=5,21710 ≈5.22
...
5.2<∛166<5.5 and ∛166=5,49586≈5.50

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