Question 139033: please help .Rationalize the denominator of the fraction 3/3 / 3/7 I am truly stumped.THe slash between the threes and the slash between the three and seven looks like a division symbol only it has a tail.hope you understand what i mean thanks for your help
Found 2 solutions by solver91311, josmiceli:
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! I presume you mean 
That 'division symbol only it has a tail' is the square root symbol. It means 'find me a number when multiplied by itself equals the number under the symbol' Unless the number under the symbol is a perfect square, like 4, 9, 16, 25..., then the square root is an irrational number. A rational number is one that can be expressed as the quotient of two integers,  where p and q are integers. An irrational number cannot be expressed this way.
So rationalizing a denominator means 'get that nasty radical (another term for the square root symbol) the heck out of my denominator'
In this problem, we need to multiply the denominator by  , so the denominator will become  . BUT, we have to do so in such a way that we don't change the value of the overall fraction. Since we know that anything multiplied by 1 is itself ( no matter what a is), we can multiply the fraction by 1 in the form of  . ( no matter what a is).
But first a rule about radicals: No matter what a and b are (as long as they are positive) we can say that  .
Now:
 .
So we have a new fraction that is equivalent to the original, but has a rational number (21) in the denominator. Done.
Answer by josmiceli(19441)  (Show Source):
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