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Question 9
Which of the following is TRUE?
$$I. \sqrt[3]{11} > \sqrt{7} > \sqrt[4]{45}$$
$$II. \sqrt{7} > \sqrt[3]{11} > \sqrt[4]{45}$$
$$III. \sqrt{7} > \sqrt[4]{45} > \sqrt[3]{11}$$
$$IV. \sqrt[4]{45} > \sqrt{7} > \sqrt[3]{11}$$
Solution
$$\sqrt[3]{11} , \sqrt{7}, \sqrt[4]{45}$$
Here $$\sqrt{7}=\sqrt[4]{49}$$
$$sqrt[4]{45}<\sqrt[4]{49}$$
Now $$sqrt[4]{45}>$$\sqrt[3]{11} since 3rd power of 45 will be greater than 4th power of 11 i.e 14631
an so $$\sqrt{7} > \sqrt[4]{45} > \sqrt[3]{11}$$
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