Question

Simplify radical 10 times radical 8

Answer 1

How can you factor 8 so it has one factor that's a perfect square?

Answer 2

would radical 8 turn into 2 radical 2?

Answer 3

good, do you see how \[\Large \sqrt{8} = 2\sqrt{2}\]

Answer 4

yes, so when i try to simplify the two together how is that done?

Answer 5

you would use the rule

\[\Large \sqrt{x}*\sqrt{y} = \sqrt{x*y}\]

Answer 6

\[\Large \sqrt{10}*\sqrt{8}\]


\[\Large \sqrt{10}*2*\sqrt{2}\]


\[\Large 2*\sqrt{10}*\sqrt{2}\]


\[\Large 2*\sqrt{10*2} \ ... \ \text{Use the rule } \sqrt{x}*\sqrt{y} = \sqrt{x*y}\]


\[\Large 2*\sqrt{20}\]


What's next?

Answer 7

its it become 2 radical 5?

Answer 8

correct, \[\Large \sqrt{20} = 2\sqrt{5}\]

making the final answer to be what?

Answer 9

2 radical 5 is not the final answer?

Answer 10

no, it helps you get there though

Answer 11

do you see how \[\Large \sqrt{20} = 2\sqrt{5}\] ??

Answer 12

yes, i see how we get that but how does this get to the final answer? Am i forgetting a number somewhere?

Answer 13

if you look back up at my steps, you'll see the last step is \[\Large 2*\sqrt{20}\]

so you're forgetting that 2* out front

Answer 14

oh, sorry so its is 4 radical 5?

Answer 15

perfect

Answer 16

an alternative way is to multiply the radicands to get 10*8 = 80, then simplify \[\large \sqrt{80}\]

Answer 17

Thank you @jim_thompson5910

Answer 18

you're welcome

Answer 19

I prefer
\[
\sqrt{10}\sqrt{8}=\sqrt{80}=\sqrt{(16) 5}=4\sqrt 5
\]

Answer 20

Thank you for showing another way @eliassaab

Answer 21

YW @Marie18