Question

Find three irrational numbers between 0.111 and
0.112

Answer 1

Step-by-step explanation:

Given :-

0.111 and 0.112

To find:-

Find three irrational numbers between 0.111 and

0.112

Solution:-

Method-1:-

Given numbers are 0.111 and 0.112

The three irrational numbers are 0.11134567...,

The three irrational numbers are 0.11134567...,0.11199882725253728..., 0.11897654329...

Method -2:-

Given numbers are 0.111 and 0.112

We know that

The irrational number between a and b is √(ab)

1)The irrational number between 0.111 and 0.112

=>√(0.111×0.112)

=> √0.012432

2)The irrational number between 0.111 and √0.012432

=> √[0.111×√0.012432 ]

=> √[√[0.012432×0.012321]]

=>√√(0.000153174672)

3) The irrational number between 0.111 and

√√(0.000153174672)

= √[0.111×√√(0.000153174672)]

=> √√√[0.000151807041×0.000153174672]

=>√√√(225×10^24)

Answer:-

The irrational numbers √0.012432,√√(0.000153174672), √√√[0.000151807041×0.000153174672]

Used formulae:-

• The irrational number between a and b is √(ab)