Question

what is radical 6r times radical 3r

Answer 1

\[\sqrt{3r} \times \sqrt{6r} = \sqrt{(6r)(3r)}\]

Answer 2

Finish simplifying from there @memy

Answer 3

By the way,

In general,

\[\sqrt{a} \times \sqrt{b} = \sqrt{ab}\]

Answer 4

\[\sqrt{18r ^{2}} = \sqrt{18 \times r ^{2}} = \sqrt{9\times2\times r ^{2}} \]

Answer 5

I made a mistake sorry :)

Answer 6

and can you do it now?

Answer 7

thank you hero and pfeh. 1999 for all your help. i understand now

Answer 8

welcome ;)

Answer 9

@memy do you know what it simplifies to? @PFEH.1999 gave you a really good hint.

Answer 10

i was thinking 3r squared radical 2 ut i may be wrong

Answer 11

Doesn't square and square root cancel? By the way radicals are the same as square root.

Answer 12

For example

\[\sqrt{a^2} = \sqrt[2]{a^2} = a\]

The square and the root cancels leaving just a.

Answer 13

So if you have

\[\sqrt{r^2}\] Do you know what that simplifies to?

Answer 14

no im confused now sorry not so good in math lol

Answer 15

As a said earlier, a radical is the same as a square root. Square roots and squares are inverses of each other. Two things that are inverses of each other usually cancel out.

Answer 16

last thing i got was 9 times 2 times r sqaured ll under the radical so i know the 9 turns into the three but the two isnt a perfect square so doesnt that have to stay under the radical/

Answer 17

Yes, but now we need to figure out what to do with the \(r^2\) that's under the radical

Answer 18

do we leave ring it out with the three and leave the two alone under the radical

Answer 19

You reduced \(\sqrt{9}\) to 3 because \(\sqrt{9}\) = \(\sqrt{3^2} = 3\)

Answer 20

Again, the root and the square also canceled in that case.

Answer 21

\(\sqrt{3^2} = 3\)
\(\sqrt{r^2} = ?\)

Answer 22

ok so if the radicals and square roots cancel out are we left with just 3 radical two
oh ok now i understand so would it e 3r radical 2 then

Answer 23

and it's good for you to know:
\[\sqrt{a ^{2}} = \pm a\]

Answer 24

r

Answer 25

for example:
\[\sqrt{9} = \pm3 \]

Answer 26

It does, but @PFEH.1999, that doesn't apply in this case. We're only concerned with positive numbers since r implies radius and the expression implies distance.

Answer 27

yes,yes you're quite write!
\[\sqrt{9} = \pm3 \]
but:
\[\sqrt{r ^{2}} = | \pm r|\]

Answer 28

sorry right not write

Answer 29

Either way, @memy has it correct now.

Answer 30

thnk you oth for your help tonight really appreciate it