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Arturiano [62]
3 years ago
9

Find the smallest value of k if 264k is a perfect square

Mathematics
1 answer:
MrRissso [65]3 years ago
4 0
Try factoring this first.
264k = 132*2k = 11*12*k = 11*3*2*2*k 
To get a perfect square, you are going to have to have an even number of prime factors. 
You have one 11 and one 3. You are going to have to do something about those two.
k = 11 * 3 <<<<< ======= answer.

Now put that into 264k and you get 11 * 3 * 2 * 2 * 11 * 3 which is a perfect square. 11^2 * 3^2 * 2^2 = 4356

The square root of 4356 = 66 
4356 is a perfect square when 33 = k.

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Step-by-step explanation:

Let's take the options one by one.

Option 1

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Option 2

If Stephanie's employers insure both of them.

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Of all the three options, the option that minimizes their expenses is when Stephanie insures herself and Jim with her employers for a total cost of $408.2 compared to a total cost of $471.09 if Jim insures the two of them with his employers or $412.94 if they respectively insure each other with their respective employers.

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