Practicing Success
Find the smallest among the following ? \(\sqrt[4]{6 },\sqrt { 2}, \sqrt[3]{4 }\) and \(\sqrt {3}\) |
\(\sqrt[4]{6 }\) \(\sqrt{2 }\) \(\sqrt[3]{4 }\) \(\sqrt{3}\) |
\(\sqrt{2 }\) |
\(\sqrt[4]{6 },\sqrt { 2}, \sqrt[3]{4 }\) and \(\sqrt {3}\) LCM of 4, 2, 3 is 12, now try to make the power same i.e.: ⇒ \(\sqrt[4]{6}\) = (6)\(\frac{1}{4}\) = (6)\(\frac{4}{12}\) = (64)\(\frac{1}{12}\) = (1296)\(\frac{1}{12}\) ⇒ \(\sqrt {2}\) = (2)\(\frac{1}{2}\) = (2)\(\frac{6}{12}\) = (26)\(\frac{1}{12}\) = (64)\(\frac{1}{12}\) ⇒ \(\sqrt[3]{4}\) = (4)\(\frac{1}{3}\) = (4)\(\frac{4}{12}\) = (44)\(\frac{1}{12}\) = (256)\(\frac{1}{12}\) ⇒ \(\sqrt {3}\) = (3)\(\frac{1}{2}\) = (3)\(\frac{6}{12}\) = (36)\(\frac{1}{12}\) = (729)\(\frac{1}{12}\) Hence, ⇒ (64)\(\frac{1}{12}\) < (256)\(\frac{1}{12}\) < (729)\(\frac{1}{12}\) < (1296)\(\frac{1}{12}\) ⇒ \(\sqrt {2}\) < \(\sqrt[3]{4}\) < \(\sqrt {3}\) < \(\sqrt[4]{6}\) Therefore, smallest no. is = \(\sqrt {2}\) |