Question

Prove that 3 is an irrational number.

Find two irrational numbers lying between 2 and 3

Answer 1

. 2 ³√(3/2) f

iii. 2 [³√(3/2)²] f

iv. 2 [³√(3/2)³] f = 2 [(3/2)] f = 3f

And there, with 2 ³√(3/2) = ³√12 and 2 ³√(3/2)² = 2 ³√(9/4) = ³√18, you have two wonderful and par excellence acoustically and musically meaningful irrational numbers between 2 and 3.

PS. Also note, upon this occasion, that 2 = ³√8and 3 = ³√27. Then check for yourselves the triple intervallic (and logarithmic) equality:

(³√27 / ³√18) = (³√18 / ³√12) = (³√12 / ³√8) = ³√(3/2)

Answer 2

you have to do the same as this