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Selina Solutions Class 9 Mathematics Solutions for Exercise 1(B) in Chapter 1 - Chapter 1- Rational and Irrational Numbers
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Write two rational numbers between √𝟐 𝒂𝒏𝒅 √𝟑.
Answer:
Let us take any two rational numbers between 2 and 3 which are perfect squares.
For example, let us consider 2.25 and 2.56.
Now, we have,
\begin{array}{l} \sqrt{2.25}=1.5 \text { and } \sqrt{2.56}=1.6 \\ \sqrt{2}<\sqrt{2.25}<\sqrt{2.56}<\sqrt{3} \\ \Rightarrow \sqrt{2}<1.5<1.6<\sqrt{3} \\ \Rightarrow \sqrt{2}<\frac{15}{10}<\frac{16}{10}<\sqrt{3} \\ \Rightarrow \sqrt{2}<\frac{3}{2}<\frac{8}{5}<\sqrt{3} \end{array}
\text { Therefore any two rational numbers between } \sqrt{2} \text { and } \sqrt{3} \text { are: } \frac{3}{2} \text { and } \frac{8}{5}
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