Question

I have to simplify some radicals... And, I think I'm starting to get the hang of it, but could someone look at my answers to see if they're right or not, and if they aren't give me a mini lesson?

Answer 1

This is what I have gotten to so far: \[\sqrt{324}=\sqrt{(18)(18)}= \sqrt{18}\times \sqrt{18}\]

Answer 2

looks good

Answer 3

What's the final answer? @jdoe0001

Answer 4

\(\bf \sqrt{324}\implies \sqrt[2]{324}\implies \sqrt[2]{18\times 18}\implies \Large \sqrt[{\color{red}{ 2}}]{18^{\color{red}{ 2}}}\)

well, what do you think we can take out of the radical?

Answer 5

recall, what comes out of the radical, is any factors that match the root

Answer 6

\(\bf \sqrt{324}\implies \sqrt[2]{324}\implies \sqrt[2]{18\times 18}\implies \Large \sqrt[{\color{red}{ 2}}]{18^{\color{red}{ 2}}}\implies 18\)

Answer 7

So it's 18 then?!

Answer 8

yeap

Answer 9

since it's exponent matches the root, it comes out

Answer 10

Thank you! @jdoe0001

Answer 11

yw

Answer 12

Could I have you check another answer?

Answer 13

@jdoe0001

Answer 14

ok

Answer 15

Is this right?\[6\sqrt{32}=6\sqrt{(8)(4)}=6\sqrt{8}\times \sqrt{4}=6\sqrt{4}\times \sqrt{8}=12\sqrt{8}\]

Answer 16

\(\bf 6\sqrt{32}\implies 6\sqrt{8\cdot 4}\implies 6\sqrt{4}\cdot \sqrt{{\color{blue}{ 8}}}\implies 6\sqrt{2^2}\cdot \sqrt{{\color{blue}{ 2^2\cdot 2}}}
\\ \quad \\
6\cdot 2\cdot 2\sqrt{2}\implies 24\sqrt{2}\)

Answer 17

That last part confuses me once you highlighted the first 8. @jdoe0001

Answer 18

\(\bf 8\implies 2\cdot 2\cdot 2\implies 2^2\cdot 2\)

Answer 19

Oh, okay. That part I've got now, but then the last part on the bottom row doesn't make sense! Can you explain what you're doing there?

Answer 20

\(\bf 6\sqrt{32}\implies 6\sqrt{8\cdot 4}\implies 6\sqrt{4}\cdot \sqrt{{\color{blue}{ 8}}}\implies 6\sqrt{2^2}\cdot \sqrt{{\color{blue}{ 2^2\cdot 2}}}
\\ \quad \\
6\sqrt{2^2}\cdot \sqrt{2^2}\cdot \sqrt{2}\implies

6\cdot 2\cdot 2\sqrt{2}\implies 24\sqrt{2}\)

Answer 21

the 2's whose exponent match the root, come out
one of the 2's is left behind, since it's not \(\bf 2^2\)

Answer 22

Okay. That was a tricky one, but I get it now, and the whole idea to do the rest of my work! Thanks again for your time! @jdoe0001

Answer 23

yw