Question 54
Which of the following relation (s) is/are true ?
I. $$\sqrt2>\sqrt[3]{3}$$
II. $$\sqrt[3]{3}>\sqrt2$$
III. $$\sqrt2=\sqrt[3]{3}$$
Solution
Terms : $$\sqrt2$$ and $$\sqrt[3]{3}$$
$$\equiv(2)^{\frac{1}{2}}$$ and $$(3)^{\frac{1}{3}}$$
L.C.M. of (2,3) = 6, thus multiplying the exponents by 6, we get :
=> $$(2)^{\frac{6}{2}}$$ and $$(3)^{\frac{6}{3}}$$
=> $$(2)^3$$ and $$(3)^2$$
=> $$8$$ and $$9$$
Now, $$9>8$$
$$\equiv\sqrt[3]{3}>\sqrt2$$
Thus, only II is true.
=> Ans - (B)
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