Medal & fan & testimonial for help with this question! Simplify: sqrt75 -4 sqrt8 -3 sqrt32?

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Medal & fan & testimonial for help with this question! Simplify: sqrt75 -4 sqrt8 -3 sqrt32?

Mathematics
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HI!!

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Other answers:

Hey, @misty1212 ! Could you help me out?(:
\[\huge\sqrt{75}-4\sqrt{8}-3\sqrt{32}\]?
Yes ma'am!
ok which one you want to do first?
nvm how about the first one
Its the whole thing that I have to simplify
\[\sqrt{75}=\sqrt{25\times 3}\] right?
Yes
that means \[\sqrt{75}=\sqrt{25}\times \sqrt{3}=5\times \sqrt{3}\] for the first one
Ohh!!
lets move on to the next one
\[\sqrt{8}=\sqrt{4\times 2}\]yes?
Yes, so 2 sqrt2?
bingo
so far we are at \[5\sqrt{3}-8\sqrt{2}\] the \(-8\) because it started at \(-4\sqrt{8}\)
Ohh okay
last one is \(-3\sqrt{32}\) which is the same as \[-3\sqrt{16\times 2}\]
then since \(\sqrt{16}=4\) you have \[-3\sqrt{16}\sqrt{2}=-3\times 4\times \sqrt{2}=-12\sqrt2\]
putting it all together (we are still not done) you get \[5\sqrt{3}-8\sqrt2-12\sqrt2\]
this is called "simplest radical form" btw
now combine like terms, since the last two both have a \(\sqrt2\) final answer is \[5\sqrt3-20\sqrt2\]
Okay, so would my final answer be 960 sqrt3
@satellite73 stop commenting and start helping !
Whaaat :/
no that is not the final answer
\[5\sqrt3-20\sqrt2\] is , as @misty1212 said
that is because \[-8\sqrt2-12\sqrt2=-20\sqrt2\]
ohhh we dont multiply.. and why does the 2 stay in the sqrt when there are two of them? Shouldnt it just canel out to be 2?
the first term has a \(\sqrt3\) in it, you can't combine it with the other two
good question! because you are adding (subtracting actually) not multiplying
it is like \[5x-8y-12y=5x-20y\] same idea you aren't multiplying anything, just combining like terms
Ohhh okay, makes sense! Thanks so much @satellite73 & @misty1212 !
yw
\[\color\magenta\heartsuit\]

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