Question

square root of 10 open parentheses 4 minus square root of 5 close parentheses plus square root of 8 open parentheses square root of 5 end root plus 2

Answer 1

\[\sqrt{10}(4-\sqrt{5})+\sqrt{8}(\sqrt{5}+2)\]

Answer 2

yes thats the problem

Answer 3

\[4\sqrt{40}-\sqrt{50}+\sqrt{40}+2\sqrt{8}\] is the first step, i.e. multiply out

Answer 4

would that be the answer ?

Answer 5

oh no we have much more work to do

Answer 6

alrighty :)

Answer 7

we can write in simplest radical form next
since \(40=4\times 10\) we have \(\sqrt{40}=\sqrt{4\times 10}=\sqrt{4}\sqrt{10}=2\sqrt{10}\)

Answer 8

i gotcha

Answer 9

similarly since \(50=25\times 2\) you have \(\sqrt{50}=5\sqrt{2}\)

Answer 10

also \(8=4\times 2\) so we have \(\sqrt{8}=2\sqrt{2}\)

Answer 11

that makes
\[4\sqrt{40}-\sqrt{50}+\sqrt{40}+2\sqrt{8}=8\sqrt{10}-5\sqrt{2}+2\sqrt{10}+4\sqrt{2}\]

Answer 12

and finally you can combine like terms
\[10\sqrt{10}-\sqrt{2}\]

Answer 13

yeah :)

Answer 14

that one is not on of my choices

Answer 15

maybe i made a mistake, let me check

Answer 16

ok:)

Answer 17

it is \(6\sqrt{10}-\sqrt{2}\) let me see why

Answer 18

oh i see my mistake

Answer 19

this line \[4\sqrt{40}-\sqrt{50}+\sqrt{40}+2\sqrt{8}\] was a mistake, it should have been
\[4\sqrt{10}-\sqrt{50}+\sqrt{40}+2\sqrt{8}\]

Answer 20

so the correct answer is \(6\sqrt{10}-\sqrt{2}\)