Multiply and simplify Radical Expression
1/2√5(1 1/2√20)

- anonymous

Multiply and simplify Radical Expression
1/2√5(1 1/2√20)

- chestercat

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- anonymous

|dw:1370239174862:dw|

- anonymous

Hi I got the answer of 7/2√5 but when I do it I get something different.

- anonymous

okay so lets write that a little prettier to deal with:\[{{1\over2}\sqrt{5}}\times{1~{1\over2}\sqrt{20}}~~\implies~~{{1\over2}\sqrt{5}}\times{{3\over2}\sqrt{20}}~~\implies~~{\sqrt{5}\over2}\times{3\sqrt{20}\over2}\]now that that looks a little better, let's solve:\[{{\sqrt{5}\times3\sqrt{20}}\over2}={3\sqrt{100}\over2}\]because 5 x 20 = 100\[3(10)\over2\]i think you've got it from here :)

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## More answers

- anonymous

oh i meant to write \[3(10)\over4\]sorry

- anonymous

I'm a bit lost I have to simplify this so would'nt 1 1/2√20 be 2 3/2√5

- anonymous

\[1 {1\over2} = {3\over2}\]\[\sqrt{20}= 2\sqrt{5}\]\[{3\over2}\times{2\over1}\sqrt{5}~~=~~{3\over\cancel{2}}\times{\cancel{2}\over1}\sqrt{5}~~=~~\large3\sqrt{5}\]

- anonymous

but the answer comes out to \[\frac{ 7 }{ 2 }\sqrt{5}\]

- anonymous

and where are you getting this from?

- anonymous

Our teacher placed the answer as \[\frac{ 7 }{ 2 }\sqrt{5}\]

- anonymous

I didn't get this answer either this is why it's confusing

- anonymous

1/2 times 3/2 = 3/4
sqrt 5 times sqrt 20 = sqrt100 = 10
3/4 times 10 = 7.5
i dont know what your teacher was doing, maybe you copied the question wrong

- anonymous

No it's printed on my paper

- anonymous

then im really not sure

- anonymous

I appreciate your help Thank you yummydum

- anonymous

no problem :)

- anonymous

I got as my final answer \[\frac{ 3 }{ 4 }\sqrt{5} \] this is why it was confusing

- anonymous

I had a person help me don't I don't believe it's correct here is why unless I'm wrong

- saifoo.khan

Alright so i read the whole problem. Where are you stuck? We should get 15/2.

- anonymous

\[1\frac{ 1 }{ 2 }\sqrt{20}\] would be \[\frac{ 3 }{ 2 }\] and \[\sqrt{20} would be 2\] add both \[2\frac{ 3 }{ 2 }\sqrt{5}\]

- anonymous

teacher has an answer of \[\frac{ 7 }{ 2 }\sqrt{5}\] could the teacher be wrong

- saifoo.khan

Yes. Teacher added the sqrt5 by misatke. Or maybe the question you wrote is incorrect.

- anonymous

question is multiply and simplify \[\frac{ 1 }{ 2 }\sqrt{5}\left( 1\frac{ 1 }{ 2 } \sqrt{20}\right)\]

- saifoo.khan

|dw:1370243682678:dw|

- anonymous

Why is this so complicated? I'm lost

- saifoo.khan

Which step is it that you don't understand?

- anonymous

how would I multiply \[\frac{ \sqrt{5} }{ 2 }\times \frac{ 3*2 }{ 2 }\sqrt{5}\] I thought you multiply numbers not square roots with numbers

- anonymous

my answer was \[\frac{ 3 }{ 4 }\sqrt{5}\] maybe this is wrong

- saifoo.khan

|dw:1370244388921:dw|

- anonymous

Wouldn't we keep the root? and just multiply getting \[\frac{ 15 }{ 2 }\sqrt{5}\]

- saifoo.khan

No ma'am.
Whenever it's given:
sqrt3 * sqrt3
we will get "3" as answer.
The roots cancel out leaving you with ONE three.

- anonymous

This is how I started
\[\frac{ 1 }{ 2 }\sqrt{5}(1\frac{1 }{ 2 }\sqrt{20})\]
\[\frac{ 1 }{ 2 }\sqrt{5}(\frac{3 }{ 2 }\sqrt{5})\]
\[\frac{ 1 }{ 2 }\times \frac{ 3 }{ 2 }=\frac{ 3 }{ 4 }\sqrt{5}\]
I know this isn't corrected but I get this

- saifoo.khan

How will you simplify sqrt 20?

- anonymous

that's right it would be 4*5 which 4 goes down to 2 so it would be \[2\sqrt{5}\]

- saifoo.khan

^

- anonymous

I forgot to add that
\[\frac{ 1 }{ 2 }\sqrt{5}(2\frac{3 }{ 2 }\sqrt{5})\]
it would be this correct and mix fractions to improper fractions would be \[2\frac{ 3 }{ 2 } would be \frac{ 7 }{ 2 }\]
\[\frac{ 1 }{ 2 }\sqrt{5}(\frac{ 7 }{ 2 }\sqrt{5})\]

- saifoo.khan

You made a mistake again. :P
It's not 2 3/2

- anonymous

so it's \[\frac{ 2 }{ 1 }X\frac{ 3 }{ 2 }\]

- saifoo.khan

No.
I think you should redo the problem. Show me yor steps please.

- anonymous

ok

- anonymous

\[\frac{ 1 }{ 2 }\sqrt{5}(1\frac{ 1 }{ 2 }\sqrt{20})\]
\[\frac{ 1 }{ 2 }\sqrt{5}(\frac{ 3 }{ 2 } 2\sqrt{5})\]
\[\frac{ 1 }{ 2 }\sqrt{5}(\frac{ 3 }{ 2 } 2\sqrt{5})\]
at this point I'm lost

- saifoo.khan

Awesome.
No the 2's on right cancels out. Right?

- anonymous

why would it cancel √20 would be 2√5 this is where I'm getting confused

- anonymous

is 2 canceling with the other 2

- saifoo.khan

sqrt(20) = sqrt(2*2*5) = 2 sqrt5
Agree?

- anonymous

yes

- saifoo.khan

Now the 2 from 2sqrt5 and the w in the denominator on the right canel out

- anonymous

I'm with you on that

- saifoo.khan

Right o what are we left with now?

- anonymous

3√5

- saifoo.khan

Right. And that is multiplied with..?

- anonymous

\[\frac{ 1 }{ 2 }\sqrt{5}\]

- saifoo.khan

Right now multiply it out.

- anonymous

\[\frac{ 1 }{ 2 }\sqrt{5}\times \frac{ 3 }{ 1 }\sqrt{5}\]
Is this looking correct?

- saifoo.khan

yes

- anonymous

\[\frac{ 3 }{ 2 }\sqrt{5}\]

- anonymous

do I take of the √ and make it \[\frac{ 3 }{ 2 }\times \frac{ 5 }{ 1 }=\frac{ 15 }{ 2 }\]

- saifoo.khan

Like a boss. (y)

- anonymous

Thanks for everything wow :.)

- anonymous

Good job helping @newatthis !!!
@saifoo.khan

- anonymous

Kudos to @yummydum too!

- saifoo.khan

@yummydum is useless.

- anonymous

No she isn't :p

- anonymous

I'M useless.

- anonymous

Yummydum isn't. Or you,for that matter.

- anonymous

Thanks for everything it helps a lot when someone knows how to guide and explain it. :)

- saifoo.khan

@help123please. believe me. I know her.
@newatthis You're welcome. :)

- anonymous

Well,yes...you've been here longer than me.

- saifoo.khan

Lol. But no doubt she has a brown brain like me! D:

- anonymous

O_O

- anonymous

Yours is a great brain,Saif.

- anonymous

U ARE 2 HELPFUL. Lol.

- saifoo.khan

And it's brown too!

- anonymous

Nope it's not.

- saifoo.khan

I'm brown. Brain is brown too. Dummy is brown too. Hence she has a brown brain too.

- anonymous

We're prolly weirding @newatthis out.
Or at least,I am.

- anonymous

:P

- anonymous

'Hence,she has a brown brain too'.
Hence. I like that word.

- saifoo.khan

Lol.

- anonymous

no I'm just doing math working my brain, or whatever is left. :)

- anonymous

Saif,I just noticed your smartscore is mine,with the numbers flipped upside down. XD

- saifoo.khan

Haha. Nice catch.

- anonymous

IKR.

- anonymous

*Flips PC upside down*
OMGEE I HAVE A 99 SS!

- saifoo.khan

Lol.

- anonymous

98% of the time,when typing lol,you're not actually laughing. Did u know? :P

- saifoo.khan

Make that 99%. I love laughing. It helps in exercising my face muscles. :P

- anonymous

Lawl.

- saifoo.khan

;)

- anonymous

so new question?
\[2x \sqrt{7}(3x \sqrt{7})\]
\[2x(3x)\sqrt{7}\sqrt{7}\]
\[6x(\sqrt{49})\]
Would this be correct?

- anonymous

sorry I just threw this in here

- anonymous

@newatthis please close this post and create a new thread.

- anonymous

2x * 3x = 6x^2 not just 6x
and √49 = 7
so now you have 6x^2 * 7 ....which is?

- anonymous

\[42x ^{2}\]

- anonymous

yes

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