Question

consider the following radicals..

Answer 1

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

Answer 2

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?

Answer 3

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

Answer 4

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

Answer 5

not squareing :) we need to get them to "look" the same:

sqrt(8) = sqrt(4*2) = sqrt(4) * sqrt(2) = 2sqrt(2)

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

does that make sense?

Answer 10

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!

Answer 11

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

Answer 12

* means multiply :)

Answer 13

gotchaa. :)

Answer 14

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

Answer 15

would some of those cancel out then?

Answer 16

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

Answer 17

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

Answer 18

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

Answer 19

lets try this......

7a + b = ?

How would you add these together considering that they are not the same variables?

Answer 20

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

Answer 21

yep!

Answer 22

so, we redefine them like this:

a = 2x b = 3x

now:
7(2x) + 3x = ?

Answer 23

okk

Answer 24

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

Answer 25

yeah. makes sense

Answer 26

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

Answer 27

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

Answer 28

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

Answer 29

ohh cuz 2 * 7 is 14 and then we add the 3..and does it stay 2 since they are both squared 2?

Answer 30

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

Answer 31

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

Answer 32

exactly :)

Answer 33

:):)

Answer 34

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?