Question

Find the smallest positive integer k such that 594 divided by the square root of k is a perfect cube

Answer 1

Answer:

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Step-by-step explanation:

Let x^3=175k

=5×5×7×k

To make 5×5×7×k a perfect cube, we are to replace k by the product of one more 5 and two more 7 at least, so that rhs will be 5×5×5×7×7×7 I.e 5^3×7^3, then x^3=(5×7)^3=35^3, hence the minimum value of k is 5×7×7=245.

Answer 2

Step-by-step explanation:

To make 5×5×7×k a perfect cube, we are to replace k by the product of one more 5 and two more 7 at least, so that rhs will be 5×5×5×7×7×7 I.e 5^3×7^3, then x^3=(5×7)^3=35^3, hence the minimum value of k is 5×7×7=245.5