Question

Arrange in ascending order of magnitude $\sqrt{3},\sqrt[5]{515},\sqrt[10]{10227}$

• A. $\sqrt[5]{515}<\sqrt[10]{10227}<\sqrt{3}$
• B. $\sqrt{3}<\sqrt[5]{515}<\sqrt[10]{10227}$
• C. $\sqrt[10]{10227}<\sqrt{3}<\sqrt[5]{515}$
• D. None of these

Answer 1

The correct option is A $\sqrt[5]{515}<\sqrt[10]{10227}<\sqrt{3}$

$\sqrt{3},\sqrt[5]{515},\sqrt[10]{10227}$

LCM of $2,5$ and $10=10$

$\sqrt{3}=\sqrt[2\times 5]{2\times 53^5}=\sqrt[10]{103\times 3\times 3\times 3\times 3}=\sqrt[10]{10243}$

$\sqrt[5]{515}=\sqrt[5\times 2]{5\times 2{15}^2}=\sqrt[10]{1015\times 15}=\sqrt[10]{10225}$

$\sqrt[10]{10227}=\sqrt[10]{10227}$

$\therefore \sqrt[5]{515}<\sqrt[10]{10227}<\sqrt{3}$