Question

find out irrational number between 0.15 to 0.16

Answer 1

hy
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irrational number - numbers which cannot be written in the p/ q form !!
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0.15 is smaller than 0.16

so irrational numbers repeat after finite number of steps !!

four irrational numbers are

1. 0.150010001
2. 0.151121112
3.0.151101110
4.0.152212221

hope helped!!
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Answer 2

When you want to find out irrational numbers between given pairs of rational numbers, then first square both the given numbers.

0.15 < 0.16
(0.15)^2 < (0.16)^2
0.0225 < 0.0256

Now simply write down those numbers between these numbers whose exact square root cannot be calculated.

0.0225 < 0.0227 < 0.0235 < 0.0239 < 0.0245 < 0.256

Now just calculate square root of all the numbers.

√0.0225 < √0.0227 < √0.0235 < √0.0239 < √0.0245 < √0.0256

On solving,

0.15 < √0.0227 < √0.0235 < √0.0239 < √0.0245 < 0.16