Dividing Radicals
To divide two radical expressions, simply write the quotient as a ratio and then
simplify. In general, we have
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.
Solution


provided that
b ≠ 0. 


Quotient rule for radicals 


Reduce. 





Rationalize the denominator. 





Note that






Quotient rule for radicals 


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.
