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Multiplying and Distributing Radical Expressions  Problem 2
Alissa Fong
Alissa Fong
MA, Stanford University
Teaching in the San Francisco Bay Area
Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts
Here I’m going to use the distributive property, but it’s a little bit tricky because I’m distributing a radical expression. That’s square root of 3x has to be multiplied by the square root of 4x and also has to be multiplied by 5, so let’s go step by step.
Square root of 3x times square root of 4x is square root of 12x², don’t forget the x squared piece, and then square root of 3x times 5 I’m going to write like this. Next thing I need to do is simplify this piece here. Square root of 12 times the square root of x² because the square root of 12 can be broken down as the square root of 4 times the square root or 3 or 2 root 3. Then the square root of x² is just plain old x. So take away 5 square roots of 3x.
The last thing I’m going to do is rearrange this so it’s written properly. What we have is 2 times x, square roots of 3 take away 5 square roots of 3x. Be really careful these guys cannot be subtracted because they have different radicands. These are not like terms, so a lot of students will lose where there are Xs they’ll get confused by the placement of the Xs. This is the final answer. It looks pretty nasty, but this is the answer to that distributing problem.
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Alissa Fong
M.A. in Secondary Mathematics, Stanford University
B.S., Stanford University
Alissa has a quirky sense of humor and a relatable personality that make it easy for students to pay attention and understand the material. She has all the math tips and tricks students are looking for.
Your tutorials are good and you have a personality as well. I hope you have more advanced college level stuff, because I like the way you teach.”
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Sample Problems (7)
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Multiplying and Distributing Radical Expressions
Problem 1 8,784 viewsMultiply:
(3√6x)(2√6x) 
Multiplying and Distributing Radical Expressions
Problem 2 7,221 viewsSimplify:
√3x(√4x − 5) 
Multiplying and Distributing Radical Expressions
Problem 3 6,232 viewsSimplify:
(4 + √6)(3 − √6) 
Multiplying and Distributing Radical Expressions
Problem 4 5,492 viewsSimplify:
(2√10 + 3√5)(√10 − 3√5) 
Multiplying and Distributing Radical Expressions
Problem 5 855 views 
Multiplying and Distributing Radical Expressions
Problem 6 1,028 views 
Multiplying and Distributing Radical Expressions
Problem 7 713 views
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