Question

i have 3 qestions, i will post in the comments

Answer 1

first: \[\sqrt{5}(8+3\sqrt{6}\]

Answer 2

\[8\sqrt{5}+3\sqrt{30}\]

Answer 3

distributive property

Answer 4

second: \[(7+\sqrt{2})(8-3\sqrt{2})\]

Answer 5

third: \[(8+\sqrt{5})(8-\sqrt{5})\]

Answer 6

and identify the conjugate of \[4+\sqrt{7}\]

Answer 7

conjugate of
\[a+\sqrt{b}\] is
\[a-\sqrt{b}\]

Answer 8

\[(8+\sqrt{5})(8-\sqrt{5})\]
\[(a+b)(a-b)=a^2-b^2\] so you get
\[(8+\sqrt{5})(8-\sqrt{5})=8^2-\sqrt{5}^2=64-5\]

Answer 9

\[(7+\sqrt{2})(8-3\sqrt{2})\]
like
\[(7+x)(8-3x)\] multiply out and see what you get