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Find the duplicate ratio of (i) \[\mathbf{2}:\text{ }\mathbf{3}\] (ii) \[\surd \mathbf{5}:\text{ }\mathbf{7}\]

(i) \[\mathbf{2}:\text{ }\mathbf{3}\]

We know that

Duplicate ratio of \[2:\text{ }3\text{ }=\text{ }{{2}^{2}}:\text{ }{{3}^{2}}~=\text{ }4:\text{ }9\]

(ii) \[\surd \mathbf{5}:\text{ }\mathbf{7}\]

We know that

Duplicate ratio of \[\surd 5:\text{ }7\text{ }=\text{ }\surd {{5}^{2}}:\text{ }{{7}^{2}}~=\text{ }5:\text{ }49\]