So, in order to rationalize the numerator, we need to get rid of all radicals that are in the numerator. Note that these are the same basic steps for rationalizing a denominator, we are just applying to the numerator now. Step 1: Multiply numerator and denominator by a radical that will get rid of the radical in the numerator. If the radical in the numerator is a square root, then you multiply by a square root that will give you a perfect square under the radical when multiplied by the numerator.
If the radical in the numerator is a cube root, then you multiply by a cube root that will give you a perfect cube under the radical when multiplied by the numerator and so forth Example 3 : Rationalize the numerator. Since we have a square root in the numerator, then we need to multiply by the square root of an expression that will give us a perfect square under the radical in the numerator.
AND Step 3: Simplify the fraction if needed. Also, we cannot take the square root of anything under the radical. Example 4 : Rationalize the numerator. Since we have a cube root in the numerator, we need to multiply by the cube root of an expression that will give us a perfect cube under the radical in the numerator. Rationalizing the Denominator with two terms Above we talked about rationalizing the denominator with one term. Again, rationalizing the denominator means to get rid of any radicals in the denominator.
Because we now have two terms, we are going to have to approach it differently than when we had one term, but the goal is still the same. Step 1: Find the conjugate of the denominator.
You find the conjugate of a binomial by changing the sign that is between the two terms, but keep the same order of the terms. Step 2: Multiply the numerator and the denominator of the fraction by the conjugate found in Step 1.
Step 3: Make sure all radicals are simplified. Step 4: Simplify the fraction if needed. Example 5 : Rationalize the denominator Step 1: Find the conjugate of the denominator.
So what would the conjugate of our denominator be? It looks like the conjugate is. No simplifying can be done on this problem so the final answer is: Example 6 : Rationalize the denominator. Practice Problems. At the link you will find the answer as well as any steps that went into finding that answer. Practice Problem 1a: Rationalize the Denominator. Practice Problem 2a: Rationalize the Numerator.
Practice Problem 3a: Rationalize the Denominator. Learn more. Why do I rationalize the numerator in this question? Ask Question. Asked 5 years, 2 months ago. Active 5 years, 2 months ago. Viewed 2k times. One of the questions is this: Rationalize the expression and simplify. There is no real other explanation, to me. As it is given, this is an indeterminate form. When one hears "rationalize" it usually means to rationalize the denominator although why in the heck that's important is something I've never understood.
So to say "rationalize" seems But the second part is "simplify" which Which just makes "rationalizing the denominator" all that much weirder. It always "unsimplifies" the expression. Add a comment. Active Oldest Votes.
Mike Pierce Mike Pierce The wording is a little strange, but I guess I should have focused on the "simplify" part more. Get step-by-step solutions from expert tutors as fast as minutes. Your first 5 questions are on us!
Cancel Proceed. Correct Answer :. Let's Try Again :. Try to further simplify. Hide Plot ». Math can be an intimidating subject. Each new topic we learn has symbols and problems we have never seen. The unknowing Sign In Sign in with Office Sign in with Facebook.
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