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Write 45 in the form k√5, where k is an integer

Can someone explain how to do this.

 Jul 3, 2016
edited by Guest  Jul 3, 2016
 #1
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The prime factorization of 45 is 5*3*3.

So, √45 can be re-written as √(5*3*3). Beacuse of order of operations, this yeilds exactly the same value as √(3^2) * √(5) .

The square root of 3 squared (√(3^2)) is 3.

Now our expression is 3√(5).

Therfore, k must be equal to 3

 Jul 3, 2016
 #2
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k cannot be an integer because this implies that a rational quantity - 45 -   would equal an irrational quantity - k√5

 

If this is what you meant, we can find "k" thusly :

 

45 = k √5   divide both sides by √5

 

45 / √5   = k

 

However......if you meant √45, then the guest's answer is correct.....

 

 

cool cool cool

 Jul 3, 2016

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