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Q. \( \sqrt[5]{3125a^{10}b^5c^{10}} \)
(a) \( 5a^2bc^2 \) (b) \( 25ab^2c \) (c) \( 5a^3bc^3 \) (d) \( 125a^2bc^2 \)
✏️ Solution
\( 3125 = 5^5 \)
\( = \sqrt[5]{5^5 \cdot a^{10} \cdot b^5 \cdot c^{10}} \)
\( = 5 \cdot a^{10/5} \cdot b^{5/5} \cdot c^{10/5} \)
\( = 5 \cdot a^2 \cdot b \cdot c^2 \)
\( = 5a^2bc^2 \)
Correct Option: (a) \( 5a^2bc^2 \)
\( \boxed{5a^2bc^2} \)