Multiplying and Distributing Radical Expressions - Concept
Multiplying rational expressions is basically two simplifying problems put together. When multiplying rationals, factor both numerators and denominators and identify equivalents of one to cancel. Dividing rational expressions is the same as multiplying with one additional step: we take the reciprocal of the second fraction and change the division to multiplication.
When you're asked to multiply or divide radicals expressions meaning they have square roots, it's a lot like distributing and foiling. Those are the ideas you're going to keep in mind. Remember foil means when you have two binomials, you multiply the first, the outers, the inners, the last, that's what foil stands for and then combine like terms.
Before you start there's a couple of things I want to show you to keep in mind. The first thing is that, if you were to see something like square root of 9 times square root of 9, you could do that problem right? Square root of 9 is 3, square root of 9 is 3, so your answer would be 9. Check it out. That was your radicand all along. Same idea with things that have non-integer square roots. Like square root of 10. Square root of 10 is some nasty decimal, I don't know what it is. But I do know that square root of 10 times square root of 10 equals regular old 10. That's really important. Or to generalise it, square root of x times square root of x equals x.
That's going to become really important when you start multiplying square roots. Again just keep in mind what you already know about distributing and use foil if you have a binomial.