What is the smallest positive integer that can be multiply by 1,008 to make it a perfect square?
A. 2
B. 3
C. 5
D. 7
E. 11
The OA is D.
I'm confused with this PS question. Experts, any suggestion about how to solve it? Thanks in advance.
What is the smallest positive integer that can be multiply..
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Hello LUANDATO.
Let's take a look at your question.
One easy way to solve this PS question is trying number by number.
Option 1: 2*1,008 = 2016, is not a perfect square.
Option 2: 3*1,008 = 3024, is not a perfect square.
Option 3: 5*1,008 = 5040, is not a perfect square.
Option 4: 7*1,008 = 7056 = (84)^2, is a perfect square.
Hence, the correct option is the option D.
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Another way to solve it is: $$1008=2^4\cdot3^2\cdot7.$$ To have a perfect square we need an even number of 2's, 3's and 7`s.
So, we need to multiply 1008 to have 2 sevens. This is why the correct option is D.
I hope these explanations may help you.
Feel free to ask me again if you have any doubt.
Regards.
Let's take a look at your question.
One easy way to solve this PS question is trying number by number.
Option 1: 2*1,008 = 2016, is not a perfect square.
Option 2: 3*1,008 = 3024, is not a perfect square.
Option 3: 5*1,008 = 5040, is not a perfect square.
Option 4: 7*1,008 = 7056 = (84)^2, is a perfect square.
Hence, the correct option is the option D.
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Another way to solve it is: $$1008=2^4\cdot3^2\cdot7.$$ To have a perfect square we need an even number of 2's, 3's and 7`s.
So, we need to multiply 1008 to have 2 sevens. This is why the correct option is D.
I hope these explanations may help you.
Feel free to ask me again if you have any doubt.
Regards.
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