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Question 102570: 
Answer by JP(22)   (Show Source):
You can put this solution on YOUR website! Ok, first you must find out what can come out, you have a first-degree root.
Let's look at sqrt14, what can you multiply together to get 14? 7*2,14*1,and that's it. Upon inspection you notice that nothing qualifies as a perfect square.
So 14 stays as it is.
Next, look at sqrt45. What multiplies together to get 45? 15*3,45*1,9*5. 9*5 are the magic numbers because of 9, 9 is a perfect square. When you take the square-root of 9 you get 3, it fits the qualifications of a first-degree root. It comes out of jail. The 5 must stay since it doesn't meet the qualifications.
You now have sqrt14/3sqrt5.
According to the rules of Roots, you cannot leave the problem in this form, so you must eliminate the root in the denominator. In order to do this you must use another rule, (when two roots with the same numbers inside the radicals are multiplied together, the radicals cancel and they become regular numbers).
So, multiply 3sqrt5 by sqrt5 and you get 3*5 left over. According to golden rule of algebra you must do to one side what you did to the other, so you must multiply sqrt5 by sqrt14 to get sqrt70.
Your solution is sqrt70/5*3 and further on to get...
sqrt70/15 as the solution
I hope this helps...
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