Multiplying Radicals

Tutoring on Multiplying Radicals

Learning Objectives:

Understand to Multiply Radicals.

Math Tutoring on Multiplying Radicals

To multiply two radical expressions with the same index multiply the coefficients together and multiply the radicands together then simplify. For example, p√u •q√v = pq√uv.

When multiplying binomials of radicals, we follow the same rules for other products involving binomial expressions, 

1.  a ( b + c ) = ab + ac 

2.  ( a + b ) ( c + d ) = ac + ad + bc + bd 

Let’s talk about conjugates now. The expression (a + √ b) and ( a - √b ) are called conjugates of each other. Another example of conjugates are ( √a + √b ) and ( √a - √b ).  Notice that they differ only in the sign between the terms, one is an addition and one is subtraction. The product of two conjugates is the difference of two squares and this result is very helpful when simplifying radical expressions that contain a sum or difference in the denominator.



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Hook Questions:

1. How do you multiply two square roots?

2. What is a conjugate in math?

3. Can you add radicals?




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