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Which value among \(\sqrt[3]{5},\sqrt[4]{6},\;\sqrt[6]{{12}},\sqrt[{12}]{{276}}\) is the largest?1). \(\sqrt[3]{5}\)2). \(\sqrt[4]{6}\)3). \(\sqrt[6]{{18}}\)4). \(\sqrt[6]{{12}}\) |
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Answer» Firstly, we have to find the L.C.M. of all the POWERS so that we can equate the bases. L.C.M. of 3, 4, 6, 12 = 12 ⇒ (5)1/3 = (54)1/12 = (625)1/12 ⇒ (6)1/4 = (63)1/12 = (216)1/12 ⇒ (12)1/6 = (122)1/12 = (144)1/12 ⇒ (276)1/12 Since, the powers are equal, we can equate the bases Hence, (5)1/3 is the largest |
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