Multiplying Radicals is Easy when you know how!

Developing the skill of multiplying radicals, depends heavily on your child having already developed the skill to apply both the commutative and associative properties of arithmetic.

If they are not comfortable with these, don't move on with this section. Please be sure they are also confident using the rules of radicals.

Be comfortable simply rearranging problems.

The 'TRICK" to multiplying radicals is to be comfortable rearranging the numbers so you can work with them!  Remember ...

(ab)(cd) = (ac)(bd)

The Associative Property of multiplication.

If you remember this when multiplying all of multiplying radicals becomes very straight forward!  

This associative property applies to any type of number.

aRootb = a multiplied by Rootb

Follow along with this worked example to see how we put this into practice.

Multiplying Radicals - Worked Example

  • Recognize that this question is in the form (ab)(cd)
  • We can rearrange to write (ac)(bd) without changing the value - associative property of multiplication.
  • Multiply the Real numbers
  • Multiply the Radicals using Rules of Radicals. Roota x Rootb = Root(ab)
  • Present your answer in a 'tidy' format.

As you can see from this worked example - the skill to multiplying radicals, is not the multiplication process, but the process of identifying the associative property of multiplication, being comfortable using this to rearrange problems, and knowing the rules of radicals.

If you are finished with this 'multiplying radicals' information, check out the rest of our Basic Algebra section or discover all the other Basic Math Material Printable Math Worksheets has to offer. 

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