Questions:
1. What are the conditions to add or subtract radical expressions?
2. Can we still operate radical expressions even if they are dissimilar to one another? What should we do for us to operate them?
3. What should we do if we have an expression with radicals at denominator? Describe briefly the process.
Answers & Comments
Answer:
1. Only when two radicals are similar may they be added or subtracted. They can be added to or taken away from in the same way as other words. Write the result of adding the numbers in front of similar radicals.
2. Only identical integers under the radical can be added or subtracted when using radicals. For instance, since one number has a 5 under the radical and the other has a 7 under the radical, 3√5 + 3√7 cannot be added or subtracted. On the other hand, 3√5 + 7√5 = 10√5.
3. A mathematical formula containing two terms and a radical in the denominator requires that both the numerator and the denominator be multiplied by the radical's conjugate. Rationalization is the name of this technique. Each radical is referred to as the other's rationalizing factor or conjugate. A monomial radical and a rational number, or a monomial radical and a difference between two different monomial radicals, is known as a binomial radical.