# Write two rational and three irrational numbers that are between 3 and 4 with explanation.

Write two rational and three irrational numbers that are between 3 and 4 with explanation.
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saiyansruleA

The given numbers are 3 and 4.
There can be many rational numbers between 3 and 4.
The given numbers can be written as $\frac{3\cdot 4}{4}=\frac{12}{4}\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}\frac{4\cdot 4}{4}=\frac{16}{4}.$
It is known that $\frac{12}{4}<\frac{13}{4}<\frac{14}{4}<\frac{15}{4}<\frac{16}{4}.$
Therefore, the two rational numbers between 3 and 4 are $\frac{13}{4}\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}\frac{14}{4}.$
The squares of the given numbers are ${3}^{2}=9$ and ${4}^{2}=16$.
So, the square-roots of all integers between 9 and 16 are irrational.
The square roots of the numbers 10,11,12,13,14 and 15 are irrational.
Therefore, the three irrational numbers between 3 and 4 are $\sqrt{10},\sqrt{11}\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}\sqrt{12}$