Answer
$-1+\sqrt 5 $
Work Step by Step
Multiply using the FOIL (first, outer, inner, last) method:
$(\sqrt 5-2)(\sqrt 5+3)=\sqrt 5 \cdot \sqrt 5+3\cdot \sqrt 5-2\cdot \sqrt 5- 2\cdot 3$
Simplify.
$=(\sqrt 5)^2+3\sqrt 5-2 \sqrt 5- 6$
$=5+3\sqrt 5-2 \sqrt 5-6$
$=-1+3\sqrt 5-2 \sqrt 5$
Factor out $\sqrt{5}$ then simplify.
$=-1+\sqrt 5(3-2) $
$=-1+\sqrt 5(1) $
$=-1+\sqrt 5 $
Hence, the correct answer is $-1+\sqrt 5 $.
