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Jenny multiplies the square root of her favorite positive integer by \(\sqrt{2}\). Her product is an integer. a) Name three numbers that could be Jenny's favorite positive integer, and explain why each could possibly be Jenny's favorite integer. b) Suppose Jenny divides the square root of her favorite positive integer by \(\sqrt2\). Does she have to get an integer? (Remember, when Jenny multiplies the square root of her favorite integer by \(\sqrt2\), she gets an integer.)

 Feb 22, 2021
 #1
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Whatever Jenny multiplies by  sqrt2 needs to be a perfect square (or 2)

    sqrt 2   * sqrt 2    =  2

     sqrt2   * sqrt   =  sqrt 16 =  4

     sqrt 2 * sqrt 32 = sqrt 64 = 8  

    

    Red numbers are her possible fav's        

 

b.    let 's   see       sqrt 2 / sqrt 2 = 1

              sqrt8 / sqrt 2 = 2

              sqrt 32/sqrt 2 = 4                    Yes she gets an integer

 Feb 22, 2021

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