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Rational and Irrational Numbers — MATHEMATICS STD 9 — Question

ICSE BoardEnglish MediumSTD 9MATHEMATICSRational and Irrational Numbers2 Marks
Question
Write in ascending order $: 6\sqrt5, 7\sqrt3$ and $8\sqrt2$
✓

Answer

$ 6 \sqrt{5}=\sqrt{6^2 \times 5}=\sqrt{180}$
$ 7 \sqrt{3}=\sqrt{7^2 \times 3}=\sqrt{147}$
$ 8 \sqrt{2}=\sqrt{8^2 \times 2}=\sqrt{128}$
and $128<147<180$
$ \therefore \sqrt{128}<\sqrt{147}<\sqrt{180}$
$ \Rightarrow 8 \sqrt{2}<7 \sqrt{3}<6 \sqrt{5}$

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