Answer
a. $2\sqrt{3}+5\sqrt{2} $.
b. $15-4\sqrt{11}$.
c. $-6\sqrt{2}-6$.
Work Step by Step
a.
$=\sqrt{2}(\sqrt{6}+5)$
Use the distributive property.
$=\sqrt{2}\cdot \sqrt{6}+\sqrt{2}\cdot 5 $
Use the multiplication property of square roots.
$=\sqrt{12}+5\sqrt{2} $
Factor out the perfect square.
$=2\sqrt{3}+5\sqrt{2} $.
b.
$=(\sqrt{11}-2)^2$
Use $(a-b)^2=a^2+b^2-2ab$.
$=(\sqrt{11})^2+(2)^2-2(\sqrt{11})(2)$
Simplify.
$=11+4-4\sqrt{11}$
$=15-4\sqrt{11}$.
c.
$=(\sqrt{6}-2\sqrt{3})(4\sqrt{3}+3\sqrt{6})$
Use the FOIL method.
$=\sqrt{6}\cdot 4\sqrt{3} +\sqrt{6}\cdot 3\sqrt6-2\sqrt{3}\cdot 4\sqrt{3}-2\sqrt3 \cdot 3\sqrt{6}$
Simplify.
$=12\sqrt{2} +18-24-18\sqrt{2}$
Add like terms.
$=-6\sqrt{2}-6$.
