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

Chelsea Kent

Mathematics

28 September, 23:32

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.

+2

Answers (1)

Know the Answer?

Selina Sherman · 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