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792 can be broken down into factors=2^3*3^2*11, so to find a multiplier that would generate a perfect square we need to supply another 2 and 11=2*11=22. Then we have the perfect square 2^4*3^2*11^2, the square root of which is 2^2*3*11=132, so the smallest multiplier is 22.

by Top Rated User (781k points)
ur mom

The prime factorization of 792 is 3^3*3^2*11^1. For an integer to be divisible by 792, its prime factorization must include 2, 3, and 11 with exponents of at least 3, 2 and 1 respectively.

For an integer to be a perfect square, the exponents in its prime factorization must be even. The smallest integer that meets this condition as well as the condition for divisibility by 792 is 2^4*3^2*11^2. This differs from 792 by having one more factor of 2 and one more factor of 11. Thus, it is 22*792 and the smallest integer Joelle could have multiplied 792 by to get a perfect square is 22.


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