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If 945*s is a perfect square then s can be which of the following numb

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Bunuel
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If 945*s is a perfect square then s can be which of the following numb [#permalink] New post   23 May 2021, 19:00
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A
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D
E

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If 945*s is a perfect square then s can be which of the following numbers?

A. 21
B. 35
C. 54
D. 105
E. 150
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D
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lalaland1234545
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Re: If 945*s is a perfect square then s can be which of the following numb [#permalink] New post   23 May 2021, 19:17
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945 = 3^3 * 5 * 7

In order to make the above number as perfect square, min power of 3, 5 and 7 you need is 3^1* 5^1 * 7^ 1

Which gives you 105

Thus, OA : D

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Re: If 945*s is a perfect square then s can be which of the following numb [#permalink] New post   24 May 2021, 00:52
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As we know, \( 945 = 3^3 * 5 * 7\)
So, for \(945*s\) to be a perfect square power of all prime factors has to be even.
Hence, the minimum value of s can be \(3*5*7=105 \) (making power of 3 as 4 and power of 5 and 7 as 2 each).
Hence the correct answer is 105.
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Re: If 945*s is a perfect square then s can be which of the following numb [#permalink] New post   24 May 2021, 09:12
prime factor everything, answer and the 945. Then you will realize you need 1'3', 1'5', and 1 '7' to make a perfect square. Only 105 provide the needed prime numbers.
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Re: If 945*s is a perfect square then s can be which of the following numb [#permalink]
24 May 2021, 09:12
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