Surd or Radical Equations

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Surd or Radical Equations
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To solve an equation with a surd
First isolate the surd
This means to get any terms not under the square
root on the other side of the equal sign
3
3
2
2
Now square both sides
You must square the whole side NOT each term. A
square "undoes" or cancels a square root
Now solve for x
1
1
You MUST check this answer
Since you squared both sides of the equation,
negatives disappear. It is possible to get an
answer that doesn't work when you plug it back in
It checks!
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Let's try another one
First isolate the surd
Remember that the 1/3 power means the same thing
as a cube root.
- 1
- 1
Now since it is a 1/3 power this means the same
as a cube root so cube both sides
3
3
Now solve for x
- 1
- 1
Let's check this answer
It checks!
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One more to see extraneous solution
The surd is already isolated
2
2
Square both sides
You must square the whole side NOT each term.
This must be FOILed
You MUST check these answers
Since you have a quadratic equation (has an x2
term) get everything on one side 0 and see if
you can factor this
Doesn't work!Extraneous
It checks!
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Acknowledgement I wish to thank Shawna Haider
from Salt Lake Community College, Utah USA for
her hard work in creating this PowerPoint. www.sl
cc.edu Shawna has kindly given permission for
this resource to be downloaded from
www.mathxtc.com and for it to be modified to suit
the Western Australian Mathematics Curriculum.
Stephen Corcoran Head of Mathematics St
Stephens School Carramar www.ststephens.wa.edu.
au