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Q. Assertion–Reason Type Question
Statement-1: \( \sqrt{7\sqrt{7\sqrt{7\sqrt{7}}}} = \sqrt[16]{7^{15}} \)
Statement-2: \( \sqrt{a\sqrt{a\sqrt{a\cdots}}} \ (n\text{ terms}) = a^{\frac{2^n – 1}{2^n}} \)
✏️ Solution
Number of nested roots = 4
Using formula:
\( = 7^{\frac{2^4 – 1}{2^4}} = 7^{\frac{16 – 1}{16}} = 7^{15/16} \)
\( = \sqrt[16]{7^{15}} \)
So Statement-1 is TRUE
Statement-2 is also TRUE
Statement-2 correctly explains Statement-1
Correct Option: (a)
\( \boxed{\text{(a)}} \)