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Multiplying Radicals of the Same Root - Problem 2

Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

Multiplying two binomials together when we have square roots involved. Multiplying two binomials if you remember is just saying like a plus b times c plus d and really the main check for this was FOIL distributing making sure each term is multiplied by each term. So we did FOIL the first, the outer, inner, last same exact approach is going to happen up here as well.

So what we need to make sure is that this 2 goes to both terms over here and this 5 root 5 goes to both terms over here as well. So 2 times 3 is 6, 2 times -2 is just -2 root 2, root 5 times 3 is just going to be 3 root 5 and then root 5 times root 2 we're multiplying square roots, the root is the same so we just multiply our terms inside so this becomes minus root 10.

Whenever you're doing a problem like this, we always want to go back and make sure we can't simplify our roots, square root of 2 can't do anything with, square root of 5 we can't do anything with that, square root of 10 is stuck as well, so what we have here is this term multiplied out in it's simplest form. Every once in a while you will get a term that can't be simplified, just simplify it as you would any other square root.

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