How would you simplify #(sqrt13 - sqrt3) ( sqrt13 + sqrt 3)#?

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Answer 1 · 2016-02-24T03:44:36

#(sqrt 13-sqrt3)(sqrt 13+sqrt 3)=10#.

#(sqrt 13-sqrt3)(sqrt 13+sqrt 3)#

This is an example of the difference of squares, #a^2-b^2=(a+b)(a-b)#, where #a=sqrt13# and #b=sqrt 3#.

Rewrite the expression as a difference of squares.

#sqrt13^2-sqrt3^2#

Apply the square root rule #sqrta^2=a#.

#13-3#

Simplify.

#10#