Question

Will someone check and help me with the next part
Multiply and simplify by factoring

Answer 1

\[\sqrt{14}\times \sqrt{6}\]

Answer 2

The first step is to combine the radicals using the product rule radicals \[\sqrt{a}\times \sqrt{b}=\sqrt{ab}\]
\[\sqrt{14}\times \sqrt{6}=\sqrt{14\times6}=\sqrt{84}\]

Answer 3

yep

Answer 4

Next,factor the radicand so that one factor is a perfect square
\[\sqrt{84}=?\]
I know what the factors of 84 is but which two do I use?
1,2,3,4,6,7,14,21,28,42,84

Answer 5

I was thinking \[\sqrt{21}\times \sqrt{4}\]

Answer 6

excellent

Answer 7

that's right, so what would you end up getting?

Answer 8

now factor into two radicals \[\sqrt{21\times4}=\sqrt{21}\times \sqrt{4}\]
finally, simplify each radical, if possible \[\sqrt{21}\times \sqrt{4}=7\sqrt{4}\]

Answer 9

remember \[2\sqrt{21}\]

Answer 10

the reason for this is that there aren't any perfect squares that go into 21

Answer 11

Thank you @Photon336