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.

Question

Mathematics

Aniyah

19 August, 05:36

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.

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Answers (1)

Know the Answer?

Sofia Barry · Answer 1

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