Question:
Arrange in descending order: \(\sqrt[4]{12}, \sqrt[3]{5}, \sqrt{3}\)
अवरोही (घटते) क्रम में व्यवस्थित कीजिए: \(\sqrt[4]{12}, \sqrt[3]{5}, \sqrt{3}\)
Options:
- \(\sqrt[4]{12}, \sqrt[3]{5}, \sqrt{3}\)
- \(\sqrt[4]{12}, \sqrt{3}, \sqrt[3]{5}\)
- \(\sqrt{3}, \sqrt[4]{12}, \sqrt[3]{5}\)
- \(\sqrt[3]{5}, \sqrt{3}, \sqrt[4]{12}\)
- \(\sqrt[4]{12}, \sqrt[3]{5}, \sqrt{3}\)
- \(\sqrt[4]{12}, \sqrt{3}, \sqrt[3]{5}\)
- \(\sqrt{3}, \sqrt[4]{12}, \sqrt[3]{5}\)
- \(\sqrt[3]{5}, \sqrt{3}, \sqrt[4]{12}\)
Correct Answer: b)
Explanation:
Raising each to their 12th power (LCM of 4, 3, 2):
\((\sqrt[4]{12})^{12} = 12^3 = 1728\)
\((\sqrt{3})^{12} = 3^6 = 729\)
\((\sqrt[3]{5})^{12} = 5^4 = 625\).
Since \(1728 > 729 > 625\), descending order is \(\sqrt[4]{12}, \sqrt{3}, \sqrt[3]{5}\).
12वीं घात लेने पर:
\((\sqrt[4]{12})^{12} = 1728\), \((\sqrt{3})^{12} = 729\), \((\sqrt[3]{5})^{12} = 625\)।
अवरोही क्रम: \(\sqrt[4]{12}, \sqrt{3}, \sqrt[3]{5}\)।