Question 101

Which value among $$\sqrt[4]{7}, \sqrt[3]{11}\ and\ \sqrt[12]{1257}\ $$is the largest ?

Solution

Terms : $$\sqrt[4]{7}, \sqrt[3]{11}\ and\ \sqrt[12]{1257}\ $$

L.C.M. of exponents (4,3,12) = 12

Multiplying the exponents by 12, we get :

$$\equiv(7)^{\frac{12}{4}},$$ $$(11)^{\frac{12}{3}}$$ and $$(1257)^{\frac{12}{12}}$$

$$\equiv(7)^3,(11)^4,(1257)^1$$

$$\equiv343,14641,1257$$

Thus, largest number = $$14641\equiv\sqrt[3]{11}$$

=> Ans - (A)

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