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
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
Was this answer helpful ?
:
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
Was this answer helpful ?
More Questions on This Topic :
Question 2.
What is the numerical value of M+F?
....
Question 3.
What is the numerical value of F?
....
Question 8.
What is the unit digit of (628−322)?
....
Latest Videos
Latest Test Papers
Submit Solution