Question 89

If $$a = \sqrt[3]{4}, b = \sqrt[4]{5}, c = \sqrt[4]{7}$$ and $$d = \sqrt[3]{9}$$, then their correct ordering is

Solution

a = $$\sqrt[\ 3]{4}\ =\ \sqrt[\ 12]{256}$$

b = $$\sqrt[\ 4]{5}\ =\ \sqrt[\ 12]{125}$$

c = $$\sqrt[\ 4]{7}\ =\ \sqrt[\ 12]{343}$$

d=$$\sqrt[\ 3]{9}\ =\ \sqrt[\ 12]{6561}$$

hence b<a<c<d


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