Dividing Radicals
To divide two radical expressions, simply write the quotient as a ratio and then
simplify. In general, we have
![](./articles_imgs/362/dividi98.gif)
provided that all expressions represent real numbers. Note that the quotient rule is
applied only to radicals that have the same index.
Example 1
Dividing radicals with the same index
Divide and simplify. Assume the variables represent positive numbers.
![](./articles_imgs/362/dividi99.gif)
Solution
![](./articles_imgs/362/dividi1.gif) |
![](./articles_imgs/362/dividi2.gif) |
provided that
b ≠ 0. |
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![](./articles_imgs/362/dividi4.gif) |
Quotient rule for radicals |
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![](./articles_imgs/362/dividi5.gif) |
Reduce. |
![](./articles_imgs/362/dividi6.gif) |
![](./articles_imgs/362/dividi7.gif) |
|
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![](./articles_imgs/362/dividi8.gif) |
Rationalize the denominator. |
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![](./articles_imgs/362/dividi9.gif) |
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![](./articles_imgs/362/dividi10.gif) |
Note that
![](./articles_imgs/362/dividi11.gif) |
![](./articles_imgs/362/dividi12.gif) |
![](./articles_imgs/362/dividi13.gif) |
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![](./articles_imgs/362/dividi14.gif) |
Quotient rule for radicals |
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![](./articles_imgs/362/dividi15.gif) |
Reduce. |
Note that in Example 1(a) we applied the quotient rule to get
In Example 1(b) we did not use the quotient rule because 2 is
not evenly divisible by 3. Instead, we rationalized the denominator to get the result
in simplified form.
|