Q: Why do you need to rationalize the denominator?

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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.

6

The idea is to get rid of the square root in the denominator. For this purpose, you must multiply numerator and denominator by the square root of 6 in this case.

1.5

If you are referring to 1/sqrt7 then you multiply the numerator and denominator by sqrt7 over sqrt7. 1 = (1)sqrt7 = sqrt7 sqrt7 (sqrt7)sqrt(7) 7

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process by which a fraction containing radicals in the denominator is rewritten to have only rational numbers in the denominator.

1

Yes, you can.

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.

-26

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.

6

No, that is not what you do.

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.

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.

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.

If you want to rationalize the denominator, then multiply numerator & denominator by sqrt(5), so 8*sqrt(5)/5 = approx 3.578