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The number of ducks in a pond is equal to the square root of the number of fish and the number of turtles is equal to the cube root of the the number of fish. The number of fish in the pond is more then 1 but less than 100 . There are no fractional or negative ducks,fish,or turtles. How many fish ducks and turtles are in the pond

Respuesta :

d = sqrt f 
t = cuberoot f    (d = ducks, f = fish and t = turtles).

so we need a number f which is a whole number between 1 and 100 and is also a perfect square and a perfect cube.  64 would suit these conditions so we might have

64 fish , 8 ducks and 4 turtles.

Answer: Number of fish = 64,

Number of ducks = 8,

Number of turtles = 4

Step-by-step explanation:

Since, the number of fish is between 1 and 100,

Also,

[tex]\text{The number of duck}=\sqrt{\text{The number of fish}}[/tex]

And,

[tex]\text{The number of fish} =\sqrt[3]{\text{The number of fish}}[/tex]

Since, the number of ducks and turtle must be a whole number.

⇒ The number of fish must be a square root and a cube root of a whole number between 1 and 100.

The numbers that are cube roots of a whole number between 1 and 100 are,

8, 27, 64

But √8 ≠ Whole number and √27 ≠ whole number.

While, √64 = 8 = A whole number.

Hence, the number of fish must be 64.

⇒ The number of duck = √64 = 8

And, the number of turtle = ∛64 = 4

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