Mathematics
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OpenStudy (anonymous):
Will post question below
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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):
\[4\sqrt{2^2*2^2*2}+6\sqrt{2*5^?}\]
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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
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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\[\sqrt{50}=\sqrt{2}\sqrt{5^2}\]
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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?
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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 \[4*4\sqrt{2}+6*\sqrt{2*5^2 }\]
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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?
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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?
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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):
\[(16+30)\sqrt{2}\]
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OpenStudy (anonymous):
So your right \[46\sqrt{2}\]
OpenStudy (anonymous):
Thank you!!
OpenStudy (anonymous):
:). np