SOLUTION: How do you rationalize and determine the denominator for this problem?
1 divided by 7times the square root of 5 minus 3times the square root of 3
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-> SOLUTION: How do you rationalize and determine the denominator for this problem?
1 divided by 7times the square root of 5 minus 3times the square root of 3
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Question 178082: How do you rationalize and determine the denominator for this problem?
1 divided by 7times the square root of 5 minus 3times the square root of 3 Answer by solver91311(24713) (Show Source):
Second way first, because that one is easier. You need to find a multiplier that will change into a rational number. will do this quite tidily.
The process is to multiply the fractional part of your expression by 1 in the form of , thus:
yielding:
then apply the LCD of 35 to get:
The other interpretation is a bit trickier, but not too.
You can't simply square the denominator because you would still end up with a two term expression one term of which would still be irrational. The trick is to remember the factorization of the difference of two squares:
are called a conjugate pair. The thing is, if you multiply a binomial by its conjugate, you get the difference of two squares.
The denominator of your expression is a binomial whose conjugate is
The process is to multiply the entire original fraction by 1 in the form of the conjugate of the denominator over itself, thus:
Yes, the answer is uglier than a mud fence, but because it has a rational number for a denominator, it is simpler than the original by definition.
