Question
Compare the following : $\frac{\sqrt{80}}{\sqrt{48}}, \frac{\sqrt{45}}{\sqrt{27}}$
✓
Answer
$\begin{array}{ll}
& \frac{\sqrt{80}}{\sqrt{48}}, \frac{\sqrt{45}}{\sqrt{27}} \\
& \sqrt{80} \times \sqrt{27}=\sqrt{2160} \\
& \sqrt{48} \times \sqrt{45}=\sqrt{2160} \\
& \text { Here, } 2160=2160 \\
\therefore \quad & \sqrt{2160}=\sqrt{2160} \\
\therefore \quad & \frac{\sqrt{80}}{\sqrt{48}}=\frac{\sqrt{45}}{\sqrt{27}}
\end{array}$
Alternate method:
$\frac{\sqrt{80}}{\sqrt{48}}, \frac{\sqrt{45}}{\sqrt{27}}$
Consider, $\frac{\sqrt{80}}{\sqrt{48}}=\frac{\sqrt{16 \times 5}}{\sqrt{16 \times 3}}=\frac{4 \sqrt{5}}{4 \sqrt{3}}=\frac{\sqrt{5}}{\sqrt{3}}$
$\frac{\sqrt{45}}{\sqrt{27}}=\frac{\sqrt{9 \times 5}}{\sqrt{9 \times 3}}=\frac{3 \sqrt{5}}{3 \sqrt{3}}=\frac{\sqrt{5}}{\sqrt{3}}$
Here, $\frac{\sqrt{5}}{\sqrt{3}}=\frac{\sqrt{5}}{\sqrt{3}}$
$\therefore \quad \frac{\sqrt{80}}{\sqrt{48}}=\frac{\sqrt{45}}{\sqrt{27}}$
& \frac{\sqrt{80}}{\sqrt{48}}, \frac{\sqrt{45}}{\sqrt{27}} \\
& \sqrt{80} \times \sqrt{27}=\sqrt{2160} \\
& \sqrt{48} \times \sqrt{45}=\sqrt{2160} \\
& \text { Here, } 2160=2160 \\
\therefore \quad & \sqrt{2160}=\sqrt{2160} \\
\therefore \quad & \frac{\sqrt{80}}{\sqrt{48}}=\frac{\sqrt{45}}{\sqrt{27}}
\end{array}$
Alternate method:
$\frac{\sqrt{80}}{\sqrt{48}}, \frac{\sqrt{45}}{\sqrt{27}}$
Consider, $\frac{\sqrt{80}}{\sqrt{48}}=\frac{\sqrt{16 \times 5}}{\sqrt{16 \times 3}}=\frac{4 \sqrt{5}}{4 \sqrt{3}}=\frac{\sqrt{5}}{\sqrt{3}}$
$\frac{\sqrt{45}}{\sqrt{27}}=\frac{\sqrt{9 \times 5}}{\sqrt{9 \times 3}}=\frac{3 \sqrt{5}}{3 \sqrt{3}}=\frac{\sqrt{5}}{\sqrt{3}}$
Here, $\frac{\sqrt{5}}{\sqrt{3}}=\frac{\sqrt{5}}{\sqrt{3}}$
$\therefore \quad \frac{\sqrt{80}}{\sqrt{48}}=\frac{\sqrt{45}}{\sqrt{27}}$
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