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Mathematics 15 Online
OpenStudy (anonymous):

Will post question below

OpenStudy (anonymous):

What is \[4\sqrt{32}+ 6\sqrt{50}\] in simplified radical form?

OpenStudy (luckycoins888):

Kk gimmeh a sec

OpenStudy (anonymous):

okay

OpenStudy (anonymous):

32= 2^5, and 50 = ??

OpenStudy (anonymous):

\[4\sqrt{2^2*2^2*2}+6\sqrt{2*5^?}\]

OpenStudy (anonymous):

square root 2 times square root 5 by the power of 2 right?

OpenStudy (luckycoins888):

-_- My laptop died

OpenStudy (anonymous):

\[4\sqrt{2^2}\sqrt{2^2}\sqrt{2}+6\sqrt{2*5^2}\]

OpenStudy (anonymous):

lol its okay

OpenStudy (luckycoins888):

-.- Let redcan help with this one xD

OpenStudy (luckycoins888):

I lost all the work i did on google docs -_________-

OpenStudy (anonymous):

Okay thanks anyway lucky

OpenStudy (luckycoins888):

Lol welcome xD

OpenStudy (luckycoins888):

Redcan you take over my internet is failing -_-

OpenStudy (anonymous):

yep\[\sqrt{50}=\sqrt{2}\sqrt{5^2}\]

OpenStudy (anonymous):

and 32 is \[\sqrt{2^{5}}\]

OpenStudy (anonymous):

Yes.

OpenStudy (anonymous):

which we can write as \[\sqrt{2^2}\sqrt{2^2}\sqrt{2}\]

OpenStudy (anonymous):

Or \[4\sqrt{2}\]

OpenStudy (anonymous):

Does this make sense?

OpenStudy (anonymous):

yes

OpenStudy (anonymous):

ok, then all we need to do is simplify the equation

OpenStudy (anonymous):

What do we have so far?

OpenStudy (anonymous):

We have \[4\sqrt{2} and \]\[\sqrt{2*5^{2}}\]

OpenStudy (anonymous):

so all together \[4*4\sqrt{2}+6*\sqrt{2*5^2 }\]

OpenStudy (anonymous):

can we simplify \[\sqrt{2}\sqrt{5^2}?\]

OpenStudy (anonymous):

yea its 50

OpenStudy (anonymous):

how about take the 5^2 out of the root? do you agree \[\sqrt{5^2}=5?\]

OpenStudy (anonymous):

umm would it be 25?

OpenStudy (anonymous):

yep, what is the square root of 25?

OpenStudy (anonymous):

5

OpenStudy (anonymous):

:), so the square root of 5^2 is 5.

OpenStudy (anonymous):

Yes

OpenStudy (anonymous):

So we can write \[4∗4\sqrt{2}+6∗5\sqrt{2}\]

OpenStudy (anonymous):

can we simplify more?

OpenStudy (anonymous):

|dw:1454370966257:dw| right?

OpenStudy (anonymous):

Sorry its messy

OpenStudy (anonymous):

Yes! now let's factor out the \[\sqrt{2}\]np, totally readable

OpenStudy (anonymous):

is it\[46\sqrt{2}\]

OpenStudy (anonymous):

\[(16+30)\sqrt{2}\]

OpenStudy (anonymous):

So your right \[46\sqrt{2}\]

OpenStudy (anonymous):

Thank you!!

OpenStudy (anonymous):

:). np

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