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!