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Question Number 208567 by Tawa11 last updated on 18/Jun/24

Answered by kgmxdd last updated on 18/Jun/24

Commented by Tawa11 last updated on 18/Jun/24

$$\mathrm{Any}\mathrm{workings}\mathrm{sir}?$$

Answered by MM42 last updated on 18/Jun/24

$$\sqrt[3]{11}=\sqrt[12]{14641}\mathrm{\&}\sqrt{7}=\sqrt[12]{117649}\mathrm{\&}\sqrt[4]{45}=\sqrt[12]{91125}$$$$\Rightarrow \left(III\right)✓$$$$$$

Commented by Tawa11 last updated on 18/Jun/24

$$\mathrm{Thanks}\mathrm{sir}$$

Answered by A5T last updated on 18/Jun/24

$$\sqrt{7}=\sqrt{\sqrt{49}}=\sqrt[4]{49}>\sqrt[4]{45}$$$$\sqrt[4]{45}\stackrel{?}{>}\sqrt[3]{11}\iff {\left(\sqrt[4]{45}\right)}^{12}={45}^3>{\left(\sqrt[3]{11}\right)}^{12}={11}^4$$$${45}^3>{\left(12\times 3\right)}^3={12}^3\times 3^3>11\times 11\times 11\times 11={11}^4$$$$\iff \sqrt[4]{45}>\sqrt[3]{11}\Rightarrow \sqrt{7}>\sqrt[45]{45}>\sqrt[3]{1}1$$

Commented by Tawa11 last updated on 18/Jun/24

$$\mathrm{Thanks}\mathrm{sir}$$

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