Question
Insert two irrational numbers between $5$ and $6.$
✓
Answer
We know that $5 = \sqrt25$ and $6 = \sqrt36.$Thus consider the numbers.
$\sqrt25 < \sqrt26 < \sqrt27 < \sqrt28 < \sqrt29 < \sqrt30 < \sqrt31 < \sqrt32 < \sqrt33 < \sqrt34 < \sqrt35 < \sqrt36.$
Therefore$, $ any two irrational numbers between $ 5 $ and $6$ is $\sqrt27$ and $\sqrt28.$
$\sqrt25 < \sqrt26 < \sqrt27 < \sqrt28 < \sqrt29 < \sqrt30 < \sqrt31 < \sqrt32 < \sqrt33 < \sqrt34 < \sqrt35 < \sqrt36.$
Therefore$, $ any two irrational numbers between $ 5 $ and $6$ is $\sqrt27$ and $\sqrt28.$
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