consider the following radicals..

- anonymous

consider the following radicals..

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- anonymous

\[7\sqrt{8}+\sqrt{18}\]

- 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

7*2sqrt(2) + 3sqrt(2) = 17sqrt(2)

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## More answers

- anonymous

oh yeah, I kind of remember how these go.. but what is the next step once we square them?

- amistre64

not squareing :) we need to get them to "look" the same:
sqrt(8) = sqrt(4*2) = sqrt(4) * sqrt(2) = 2sqrt(2)

- amistre64

sqrt(18) = sqrt(9*2) = sqrt(9) * sqrt(2) = 3sqrt(2)

- amistre64

now we can combine these puppies since they are both "sqrt(2)"s

- amistre64

7*2sqrt(2) + 3sqrt(2) = 14sqrt(2) + 3 sqrt(2) = 17sqrt(2)

- amistre64

does that make sense?

- 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

\[\sqrt{ab} = \sqrt{a}* \sqrt{b}\]

- amistre64

* means multiply :)

- anonymous

gotchaa. :)

- amistre64

\[\sqrt{8}=\sqrt{4*2}=\sqrt{4} * \sqrt{2} = 2\sqrt{2}\]

- anonymous

would some of those cancel out then?

- amistre64

nope, since the problem calls for addition, the only way to cancel anything out would be to subtract like amounts.

- anonymous

wait. sorry I just realized you were giving an example. ha okk

- 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

lets try this......
7a + b = ?
How would you add these together considering that they are not the same variables?

- amistre64

we would have to redefine the variables so that they were the same.... right?

- anonymous

yep!

- amistre64

so, we redefine them like this:
a = 2x b = 3x
now:
7(2x) + 3x = ?

- anonymous

okk

- amistre64

14x + 3x = 17x... right? not trying to solve for x....just trying to add them together

- anonymous

yeah. makes sense

- amistre64

radicals act just like these variables...... we have to redefine them to "match" each other before we can add them up.

- amistre64

\[7\sqrt{8} + \sqrt{18}\]\[7(2\sqrt{2}) + 3\sqrt{2} = ?\]

- amistre64

now that they are the "same" variable...we can add them up\[17\sqrt{2}\]

- 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

yep... and the so-called "variable" is the sqrt(2) part.

- anonymous

okk thanks so much for walking through that! so the answer is \[17\sqrt{2}\]

- amistre64

exactly :)

- 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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