Find the smallest among the following:
\(\sqrt[4]{6},\ \sqrt{2},\ \sqrt[3]{4}\) and \(\sqrt{3}\)
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\sqrt{2}\)
Roots of different orders cannot be compared directly. Raising every number to the LCM of the orders, here LCM(4, 2, 3, 2) \(=12\), removes all the roots, and the order of the numbers does not change.
\(\left(\sqrt[4]{6}\right)^{12}=6^{3}=216\)
\(\left(\sqrt{2}\right)^{12}=2^{6}=64\)
\(\left(\sqrt[3]{4}\right)^{12}=4^{4}=256\)
\(\left(\sqrt{3}\right)^{12}=3^{6}=729\)
The smallest result, 64, belongs to \(\sqrt{2}\).