anonymous
  • anonymous
consider the following radicals..
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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anonymous
  • anonymous
\[7\sqrt{8}+\sqrt{18}\]
amistre64
  • amistre64
radicals are like variables in this case, in order to add them together they have to be "identical" can we reduce these radical expressions to have the same radical stuff?
amistre64
  • amistre64
7*2sqrt(2) + 3sqrt(2) = 17sqrt(2)

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anonymous
  • anonymous
oh yeah, I kind of remember how these go.. but what is the next step once we square them?
amistre64
  • amistre64
not squareing :) we need to get them to "look" the same: sqrt(8) = sqrt(4*2) = sqrt(4) * sqrt(2) = 2sqrt(2)
amistre64
  • amistre64
sqrt(18) = sqrt(9*2) = sqrt(9) * sqrt(2) = 3sqrt(2)
amistre64
  • amistre64
now we can combine these puppies since they are both "sqrt(2)"s
amistre64
  • amistre64
7*2sqrt(2) + 3sqrt(2) = 14sqrt(2) + 3 sqrt(2) = 17sqrt(2)
amistre64
  • amistre64
does that make sense?
anonymous
  • anonymous
yeah I kind of understand where it's going. Does the *=x? ha.. i'm definitely a visual learner so that is helpful to write out. Thanks!
amistre64
  • amistre64
\[\sqrt{ab} = \sqrt{a}* \sqrt{b}\]
amistre64
  • amistre64
* means multiply :)
anonymous
  • anonymous
gotchaa. :)
amistre64
  • amistre64
\[\sqrt{8}=\sqrt{4*2}=\sqrt{4} * \sqrt{2} = 2\sqrt{2}\]
anonymous
  • anonymous
would some of those cancel out then?
amistre64
  • amistre64
nope, since the problem calls for addition, the only way to cancel anything out would be to subtract like amounts.
anonymous
  • anonymous
wait. sorry I just realized you were giving an example. ha okk
anonymous
  • anonymous
ok. So which side do we want to subtract from? Sorry, i don't know what the format of this answer should even look like really so i'm a little confused
amistre64
  • amistre64
lets try this...... 7a + b = ? How would you add these together considering that they are not the same variables?
amistre64
  • amistre64
we would have to redefine the variables so that they were the same.... right?
anonymous
  • anonymous
yep!
amistre64
  • amistre64
so, we redefine them like this: a = 2x b = 3x now: 7(2x) + 3x = ?
anonymous
  • anonymous
okk
amistre64
  • amistre64
14x + 3x = 17x... right? not trying to solve for x....just trying to add them together
anonymous
  • anonymous
yeah. makes sense
amistre64
  • amistre64
radicals act just like these variables...... we have to redefine them to "match" each other before we can add them up.
amistre64
  • amistre64
\[7\sqrt{8} + \sqrt{18}\]\[7(2\sqrt{2}) + 3\sqrt{2} = ?\]
amistre64
  • amistre64
now that they are the "same" variable...we can add them up\[17\sqrt{2}\]
anonymous
  • anonymous
ohh cuz 2 * 7 is 14 and then we add the 3..and does it stay 2 since they are both squared 2?
amistre64
  • amistre64
yep... and the so-called "variable" is the sqrt(2) part.
anonymous
  • anonymous
okk thanks so much for walking through that! so the answer is \[17\sqrt{2}\]
amistre64
  • amistre64
exactly :)
anonymous
  • anonymous
:):)
anonymous
  • anonymous
quick question..again.. to find the product for (5+3i)(5-3i) would this just be 10? I think the 3i's would cancel out?

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