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39 votes
39 votes
Find the smallest value of k such that 54k is a perfect square.

User Richard Jordan
by
2.6k points

1 Answer

27 votes
27 votes

Answer: 6

Explanation:

From the prime factorization of 54 you get:

54 = 2×3×3×3

So ,

You can write it as,

54 = 2×3^2×3,

Make sure all of the factors are in square form, so we add a another 2 and a three to the factors to make them all in square form

You get

=2×3^2×3×2×3 (the last 2×3 is added because one 2 and 3 were not having another pair so they were added to make them squares)

So k is basically 2×3 which is 6

And 54×6 gives us 324, which is a perfect square.

User Alex Siepman
by
2.9k points