I'm writing the answer but Bunuel is too fast to reply, a machine
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\((5@45)@60 =(\sqrt{5*45})@60=(\sqrt{225})@60=15@60=\sqrt{15*60}=30\).

Answer: A.
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I tried to keep the numbers as manageable as possible and use numbers that I knew the perfect squares of.

\((5@45)@60\)= \(\sqrt{5*(5*9)}\) \(=5*3=15\)

\(15@60=\) \(\sqrt{(3*5)*(3*4*5)}\) \(= 3*5*2= 30\)

We are given that the operation @ is defined by x@y = √(xy) for all positive numbers.

We are next given that (5@45)@60. Following PEMDAS rules, we want to begin with the operation inside the parentheses. According to the operation, x will be replaced with 5, and y will be replaced with 45. Thus, we have:

5@45 = √(5 *45) = √225 = 15

We have determined that (5@45) = 15, so we substitute 15 for (5@45) to obtain 15@60.

According to the operation, x will now be replaced with 15 and y will now be replaced with 60. Thus we have:

15@60 = √(15*60) = √900 = 30

The answer is A.
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What is the point of these questions? I don't get what is being tested here

I call these "Strange Operator" questions.
We want to evaluate: (5 @ 45) @ 60

Start with (5 @ 45)
(5 @ 45) = √[(5)(45)]
= √225
= 15


So, (5 @ 45) @ 60 = 15 @ 60
From here, 15 @ 60 = √[(15)(60)]
= √900
= 30

Answer: A
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