SOLUTION: "find the smallest whole number that should be multiplied to each of the following so that the product is a square number? a)48 b)54 c)108 d)150

Question 985153: "find the smallest whole number that should be multiplied to each of the following so that the product is a square number? a)48 b)54 c)108 d)150
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

In order to be a perfect square, all prime factors of a number must be represented an even number of times.

The prime factorization of 48 is

. You have an even number of factors of 2, but only 1 factor of 3. If you include another factor of 3, then there will be four 2s and two 3s, which results in 48 times 3 or 144. 144 is indeed a perfect square.

Do the other problems the same way. By the way, next time read and follow instructions: One problem per post.

John

My calculator said it, I believe it, that settles it

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