3.4 Simplifying Radicals
MCR3U
Radical Mathematics
Some vocabulary before we get started...
An entire radical is one with a coefficient of 1.
For example:
A mixed radical is one with a coefficient other than 1.
For example:
Like radicals have the same number under the radical sign.
For example:
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is t e fo the g
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ica s sym ric l si
gn bol .
When multiplying radicals...
For example:
When multiplying mixed radicals...
For example:
Hwmk ­ P.167 #1cd,2cd,3cd,4ace,5ace,6bf,7acef,8,11,12
1
3.4 Simplifying Radicals
MCR3U
To simplify a radical, we re­write the entire radical as the product of other radicals, ensuring one of the radicals is a perfect square.
For example:
Simplify:
Multiplying Radicals
Hwmk ­ P.167 #1cd,2cd,3cd,4ace,5ace,6bf,7acef,8,11,12
2
3.4 Simplifying Radicals
MCR3U
Adding Radicals
Arithmetic operations with radicals behaves much like other algebraic operations. We will simplify, apply the distributive property and collect like terms.
For example...
Simplify:
Hwmk ­ P.167 #1cd,2cd,3cd,4ace,5ace,6bf,7acef,8,11,12
3