How do you simplify surds in brackets?

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Answer 1 · 2018-01-05T11:16:56

To simplify a surd, separate the two factors using to multiply the entire bracket or multiply directly...

Lets use the following example for more explanation..

E.g Expand and Simplify..

#(3 + sqrt2) (3 - sqrt2)#

First Method!

#(3 + sqrt2) (3 - sqrt2)#

#3 (3 - sqrt2) + sqrt2 (3 - sqrt2)#

#9 -6sqrt2 + 6sqrt2 -2#

Collecting like terms..

#9 - 2 - 6sqrt2 + 6sqrt2#

#7 + 0#

#7#

Second Method!

#(3 + sqrt2) (3 - sqrt2)#

#(3 xx 3) + (3 xx -sqrt2) + (sqrt2 xx 3) + (sqrt2 xx- sqrt2)#

#9 + (-6sqrt2) + 6sqrt2 + (-2)#

#9 - 6sqrt2 + 6sqrt2 - 2#

#9 + 0 - 2#

#7#

Hope this helps!