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Q. If \( \sqrt[x]{3} \times \sqrt[y]{5} = 10125 \), find \( 12xy \)
(a) 1 (b) \( \frac{1}{3} \) (c) 2 (d) \( \frac{1}{2} \)
✏️ Solution
\( \sqrt[x]{3} = 3^{1/x},\quad \sqrt[y]{5} = 5^{1/y} \)
\( 3^{1/x} \cdot 5^{1/y} = 10125 \)
\( 10125 = 3^4 \cdot 5^3 \)
Compare powers:
\( \frac{1}{x} = 4,\quad \frac{1}{y} = 3 \)
\( x = \frac{1}{4},\quad y = \frac{1}{3} \)
\( 12xy = 12 \cdot \frac{1}{4} \cdot \frac{1}{3} \)
\( = 1 \)
Correct Option: (a) 1
\( \boxed{1} \)