Question

I think I got it.
Simplify the radical expression.

Answer 1

i chose 16

Answer 2

not really.

Answer 3

Are there any options?

Answer 4

10 and 16

Answer 5

Okay the answer isn't 16 because the square root of 16 can be simplified to?

Answer 6

8

Answer 7

And it would not be

Answer 8

So what other option has 8?

Answer 9

b :) thanks

Answer 10

Remember that a perfect square is for example 8*8 which is 64. 64 times what equals 128? Then remember to bring the perfect square outside of the radical because it "undoes it" basically :P

Answer 11

Yes 8 √ 2 is the answer but you do understand why right?

Answer 12

kinda im getting there

Answer 13

Like jtug said you start off with 128 right? Than what I do is divided 128 by 2 and you get 64. 8x8 is 64 :) So thats why you get 8√ 2

Answer 14

you made it so clear i get it now

Answer 15

Your welcome :) and I gave Jtug a medal cause he helped!

Answer 16

Thank you! same to you

Answer 17

wait so do I always divided by 2?

Answer 18

I have one with 500 and I divided it by 2 and got 250 so what do I do now?

Answer 19

Well it depends. You have to basically try to take it apart piece by piece until you can get a perfect square. If you end with more than 1 perfect square, multiply them because interestingly enough it becomes just a bigger perfect square. Then you can find out which number times that same number equals that "bigger perfect square"

Answer 20

Yeah like Jtug said i usually do just because its a start to simplifying, but than you have to find a perfect square root so it all depends on what the problem is

Answer 21

Ok, so 500 for example. You divided by 2 and it gave you 250. Do it again you have 125 * 2 * 2 right? Well, 2*2 = 4 which is a perfect square. Now we have 4 * 125. So now we already have 1 perfect square BUT we still have to take apart 125. What common factor can go into 125, 5 times?

Answer 22

Because 125 is only divisible by 5 or 1 fyi

Answer 23

25

Answer 24

Yes! So, now we have 4 * 25 * 5 which still equals 500.

Answer 25

Out of those three, which are perfect squares?

Answer 26

4 and 5?

Answer 27

Not quite. 4 is correct but why couldnt it be perhaps the 25? what times what = 25?

Answer 28

5&5

Answer 29

Okay Jtug looks like you got this one good job :) Raven if you need me just tag me :D Bye

Answer 30

Thanks! Sorry I kinda took this one over. I'll let you have the rest for awhile XD

Answer 31

And yes! It's 5*5 = 25 so that must mean 25 is the perfect square. Perfect squares are only made when its a whole number times a whole number just so you know. 5 can only be made when its like, 2.23 * 2.23 which clearly aren't whole numbers

Answer 32

So, 4 and 25 are perfect squares? What did I mention about having more than 1 perfect square?

Answer 33

divide?

Answer 34

Mmmmm opposite of it. Because if you multiply them it becomes one giant perfect square. So what is 25*4? And then what do you do with that value since its underneath the radical?

Answer 35

90 and muliply

Answer 36

Check your math again. What's 25 times 4?

Answer 37

100

Answer 38

Aha. And now we have a bigger perfect square. So now we have 100*5 which still equals 500. So now what do you do with the 100 since it's a perfect square and underneath the radical?

Answer 39

IM not for sure

Answer 40

Okay, well, if you'd like to think of it like this the square root (underneath radical) of 100 is 10, because 10 times 10 is 100. Alternatively with 25*4*5 we can say the square root of 25 and 4 is 5 and 2 which we then multiply to give us the same value, 10. So what do we do with 10 if we know that the remainder in the square root is 5?

Answer 41

Yes!!!

Answer 42

ohh thanks

Answer 43

i have another one

Answer 44

and heres a simple way to put it back together. We can take the 10 from the outside and multiply it by itsself to get 10*10 = 100 right? Now we put the 100 in the radical and multiply it by 5, which gives us the original square root of 500.

Answer 45

Simplify the expression.

Answer 46

@GoodVibess

Answer 47

Ah. Remember what is common? Also that it's addition so what do we do with 6 and 5 again?

Answer 48

Oh hi sorry I was on a different question

Answer 49

the 6 and multiply it?

Answer 50

Not quite it's addition and the radicals are common so we ____?

Answer 51

\[500=2^2 5^3 \] from Mathematica's FactorInteger function.

Answer 52

Sorry Raven I forgot how to divide Square Roots :/

Answer 53

add

Answer 54

Yes! So 6+5= 11 and the 6 doesnt contain a perfect square so it stays the same. So what does it look like altogether?