√x = ³√y
⇒  x^1/2 = y^1/3
⇒  (x^1/2)⁶ = (y^1/3)⁶
⇒  x³ = y²

Correct Option: A

√x = ³√y
⇒  x^1/2 = y^1/3
⇒  (x^1/2)⁶ = (y^1/3)⁶
⇒  x³ = y²

The number = 90 × A
= 3 × 3 × 2 × 5 × A
The least value of A for which the given number is a perfect cube
= 3 × 2² × 5²
= 3 × 4 × 25 = 300

Correct Option: D

The number = 90 × A
= 3 × 3 × 2 × 5 × A
The least value of A for which the given number is a perfect cube
= 3 × 2² × 5²
= 3 × 4 × 25 = 300

Let number be x
∴  According to question,
x³ − x² = 48     ∴  x = 4

Correct Option: D

Let number be x
∴  According to question,
x³ − x² = 48     ∴  x = 4

343 = 7 × 7 × 7
125 = 5 × 5 × 5
81 = 3 × 3 × 3 × 3
64 = 8 × 8 = 4 × 4 × 4
We see that 343 and 125 are only perfect cubes of 7 and 5 respectively. 81 is only a perfect square of 9. 64 is a perfect square of 8 as well as a perfect cube of 4.

Correct Option: D

343 = 7 × 7 × 7
125 = 5 × 5 × 5
81 = 3 × 3 × 3 × 3
64 = 8 × 8 = 4 × 4 × 4
We see that 343 and 125 are only perfect cubes of 7 and 5 respectively. 81 is only a perfect square of 9. 64 is a perfect square of 8 as well as a perfect cube of 4.

4320 = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 5
= 2³ × 3³ × 2² × 5
∴  Required number = 2 × 5 × 5 = 50

Correct Option: B

4320 = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 5
= 2³ × 3³ × 2² × 5
∴  Required number = 2 × 5 × 5 = 50