Question

12 Find the smallest number by which 200 must be multiplied so that the product is a perfect cube

Answer 1

firstly let us split 200 into prime factors

200

=

100×2

200 = 50×2×2

200 = 25×2×2×2

200 = 5×5×2×2×2

200=52×23

for a cubed number all the powers must be multiples of 3

The power of 2 is 3 which is a multiple of 3

The power of 5 is 2 which is not. We need another 5 to make 53

So the smallest number to multiply 200 by to get a cube number is 5.

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Answer 2

$\huge\star\boxed\boxed\pink{{ ANSWER}}$

IT MUST NE MULTIPLIED BY 5 TO GET A PERFECT CUBE.

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$200 \times 5 = 1000 \\ \sqrt[3]{1000} = 10$