Question

12. The least possible value of A for which 90 x A is
a perfect cube is
(a) 200
(b) 300
(c) 500
(d) 600​

Answer 1

Answer

answer: 90=9×10=3×3×2×5=3²×2¹×5¹

thus, the least possible value of A will

be X<A i.e make the triplets of the factors

of 90 then we get

3×3×3×2×2×2×5×5×5=3³×5³×2³

Now, the least value of A will be,

=[{(3³/3²)(5³/5)(2³/2)}]

=3(5²)(2²)

=3×5²×2²

=3×25×4

=10²(3)

=300

Answer 2

Step-by-step explanation:

the number= 90×A

=3×3×2×5×A

now the least value of A for which the given number is a perfect cube = 3× (2)²×(5)²

=3×4×25

=300.

And the answer is option (B) 300.