How do you simplify #sqrt(1+x) * sqrt(1-x)#?

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Answer 1 · 2018-07-17T09:35:03

#sqrt(1 -x^2)#

Apply rule: #sqrt(a).sqrt(b)# = #sqrt(ab)#

#sqrt(1+x).sqrt(1-x)#

#sqrt((1+x).(1-x))#

We know that:
#(a + b).(a-b)# = #a^2-b^2#

So we get:

#sqrt((1+x).(1-x))#

#sqrt(1 -x^2)#

Hope this helps!