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You multiply the numerator and the denominator by the same expression - and do it in such a way that the denominator becomes rational.Example 1: The denominator is square root of 5, which I will call root(5). If you multiply top and bottom by root(5), the denominator will become rational.
Example 2: The denominator is root(2) + root(3). If you multiply top and bottom by root(2) - root(3), then the denominator will become rational.
- You multiply both, the numerator and the denominator, of the fraction by the complex conjugate of the denominator. The complex conjugate of (x + iy) is (x - iy). Thus (u + iv)/(x + iy) =[(u + iv)*(x - iy)]/[(x + iy)*(x - iy)] and the denominator is then x2 -ixy + ixy - i2y2 = x2 + y2 which is real but it may or may not be rational.
- If this denominator is irrational, you can rationalise is by a similar process, using the irrational conjugate. For [p + sqrt(q)], it is [p - sqrt(q)].
There are denominators which cannot be rationalised. For example 3/pi.
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Can you use conjugates to rationalize the denominator even when the denominator contains two radical terms?
Yes. The original denominator and its conjugate will form the factors of a Difference of Two Squares (DOTS) and that will rationalise the denominator but only if the radicals are SQUARE roots.
To rationalize a denominator that has more than one term you multiply the fraction by where B is the conjugate of the denominator.?
Yes, that is correct.
What is the importance of the conjugate in rationalizing the denominator of a rational expression that has a radical expression in the denominator?
To eliminate the radical in the denominator.
What is true about both the numerator and denominator of rational expressions?
Both the numerator and denominator are polynomials
Common denominator for numbers 3 5 7?
1 is the only common denominator.
What is rationalize a denominator?
process by which a fraction containing radicals in the denominator is rewritten to have only rational numbers in the denominator.
Why do you need to rationalize the denominator?
It is basically a convention for a standardized form.
To get rid of radicals in the denominator of a fraction you should rationalize the denominator by multiplying the fraction by a helpful form of?
1
Can you rationalize a denominator with more than one radical term?
Yes, you can.
You can only use conjugates to rationalize the denominator when the denominator contains one radical term?
No, you can also use conjugates with more than one radical term. For example, if the denominator is root(2) + root(3), you can use the conjugate root(2) - root(3) to rationalize the denominator.
Rationalize the denominator -8 divided by the square root of 18x?
-26
Why rationalize a denominator?
You rationalize a denominator in a question because having a irrational root makes it harder to work with then a irrational in the numerator. I've never heard anyone question it and it is not hard to remove an irrational root. All you have to do is multiply the top and bottom by its conjugate.
What is the rationalizes denominator of 42 divided by the square root of 7?
6
To rationalize a denominator that has more than one term you multiply the fraction by bb where B is the conjugate of the numerator?
No, that is not what you do.
What does it mean to rationalize a denominator?
Sometimes the denominator is an irrational or complex number (depending on the level that you are at). Rationalising the denominator requires to multiply both the numerator and denominator of the fraction by a suitable number - usually the conjugate - so that when simplified, the denominator is rational - normally an integer.
How do you rationalize the denominator of a radical expression that has two terms in the denominator?
You multiply the numerator and the denominator by the "conjugate" of the denominator. For example, if the denominator is root(2) + root(3), you multiply top and bottom by root(2) - root(3). This will eliminate the roots in the denonimator.
Can you use conjugates to rationalize the denominator even when the denominator contains two radical terms?
Yes. The original denominator and its conjugate will form the factors of a Difference of Two Squares (DOTS) and that will rationalise the denominator but only if the radicals are SQUARE roots.
