Question
Download Solution PDF\(\text{Simplify:} \quad \sqrt[6]{729} + \sqrt[4]{65536} + \sqrt[3]{5832} + \sqrt{1764} \)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Simplify: √6(729) + √4(65536) + ∛(5832) + √(1764)
Formula used:
1. √n(x) = x1/n
2. ∛(x) = x1/3
3. √(x) = x1/2
Calculation:
√6(729) = 7291/6
⇒ 729 = 36
⇒ 7291/6 = 3
√4(65536) = 655361/4
⇒ 65536 = 216
⇒ 655361/4 = 24 = 16
∛(5832) = 58321/3
⇒ 5832 = 183
⇒ 58321/3 = 18
√(1764) = 17641/2
⇒ 1764 = 422
⇒ 17641/2 = 42
Adding all:
⇒ 3 + 16 + 18 + 42 = 79
∴ The correct answer is option (1).
Last updated on Jul 17, 2025
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