Question
x is the smallest number such that x2 is a perfect square and is x3 is a perfect cube. Then, the number of divisors of x is
Answer: Option C
:
C
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C
x2 is a perfect square ⇒x2=a2. x3 is a perfect cube ⇒x3=b3. x2×x3=a2×b3⇒x=√6a2b3=ab√6b.
For x to be a natural number; 6b has to be a perfect square ⇒b=6⇒x=23×34⇒ number of divisors =20
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