Which of the following relation (s) is/are true ? I. \sqrt2>\sqrt[3]{3} II. \sqrt[3]{3}>\sqrt2 III. \sqrt2=\sqrt[3]{3}

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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