got a math question (square root-related)

[Ksandra]

so I work as a tutor and I have this one HS student who argues about EVERYTHING. He's a good kid, but that part drives me nuts. Anyways I am the English/HW club tutor and the math tutor/expert doesn't work on Wednesdays, and this kid had to do some algebra homework. Math had to be my least favorite subject in school, so I usually don't remember the stuff, I have to look it up to help the HS kids. So basically the student had to do this:

8√2 X 2

The owner and I couldn't quite remember how to do it so looked it up and found the easy way which is multiply the whole numbers then multiply the roots, giving the answer:

16√2


The student however couldn't let it go. I guess his teacher is teaching them to convert the whole number into the root, then multiplying it, then simplifying.

First of all, I kinda doubt that's what his teacher taught him, the student has had a habit in the past of doing overly complicated ways of solving problems, and always insists the teacher told him to do it that way.

In any case, his method always gave him the answer of just 16. We told him that was impossible and he kept saying "I know my math is right, and that's how the teacher taught us." Unfortunately, because above is the simplest method it was the only way I could find out to do it online.

So, I'm wondering for you math buffs if someone can show me step by step how you convert 8√2 into just a square root, then multiply it by 2, then simplify it back. I told the student to ask his teacher tomorrow, but as I said this is a common occurrence with him, and I have a strong feeling he won't ask, yet continue to argue with us over it.

[Jaybar]

He thinks the 'x2' is under the square root as well (Square root of 4 is 2, multiplied by 8 is 16, which I believe is where he is getting the answer). The example you gave clearly shows that the 'x2' is outside the square root.

I know that the original square root was (Sorry I don't know the shortcut for the symbol) SqRt(64x2) if I remember my simple algebra right ;x

I can't remember how to multiply SqRts together, sadly (Edit, I do ;x). But it would be SqRt(128 ) x SqRt(4). I would think you could multiply them together as is, giving SqRt(128x4) = SqRt(512).

Yea pretty sure that's how you do it. If you start to find some multiples, you can get SqRt(64x8 ) = SqRt(64x4x2). There are only 2 squares inside, so you can pull them out and get (8x2)SqRt(2), which is how you got 16SqRt(2).

[Ksandra]

He thinks the 'x2' is under the square root as well (Square root of 4 is 2, multiplied by 8 is 16, which I believe is where he is getting the answer). The example you gave clearly shows that the 'x2' is outside the square root.

I know that the original square root was (Sorry I don't know the shortcut for the symbol) SqRt(64x2) if I remember my simple algebra right ;x

I'm going to try and replicate it though I don't remember the exact numbers he was using. (note: √ = alt + 251)


I THINK what he did was took 8√2 and converted it by doing 8^2= 16 then multiplying it by 8 (not sure why) to get √128

Since we need two he then did √128 + √128 to get √256 then he simplified the root and got 16.


I'm guessing his mistake when doing this is in where he converted 8√2 to √128, but again I don't know how to do this stuff so not sure.

[Jaybar]

Yea that's essentially the complicated way of how I thought he did it, lol.

[Ksandra]

ah ha! thanks! I think I get it because you multiply the wholes by wholes and the roots by roots in order to do it his way both numbers need to be in root form right? Yay I'll be sure to remember that for tomorrow. :O

[Woozie]

Is it 8*sqrt(2)*2 or is it 8*sqrt(2*2)? They way you have it written, it's hard to tell.

If it's the first, then the simplest form would simply be 16*sqrt(2) [just multiply the 8 and the 2, just as you did]. No form is going to be simpler than that.

If it's the second, then it would be 8*sqrt(2*2)=8*sqrt(4)=8*2=16, and the student would be correct.

I'm thinking it's the second way, because the first way would be pointless as a homework problem.

Edit: For the sake of clarity, use parenthesis when typing roots that way. For example 4=√(10+6) instead of 4=√10+6.

[Jaybar]

Yea, likes times likes. Hmm I think I owe my math teachers an apology.

[Ksandra]

Is it 8*sqrt(2)*2 or is it 8*sqrt(2*2)? They way you have it written, it's hard to tell.

If it's the first, then the simplest form would simply be 16*sqrt(2) [just multiply the 8 and the 2, just as you did]. No form is going to be simpler than that.

If it's the second, then it would be 8*sqrt(2*2)=8*sqrt(4)=8*2=16, and the student would be correct.

I'm thinking it's the second way, because the first way would be pointless as a homework problem.

Edit: For the sake of clarity, use parenthesis when typing roots that way. For example 4=√(10+6) instead of 4=√10*6

it was (8√2) X 2 so the first way. And not really pointless, there was more to the problem but the other parts were irrelevant to my question (he was finding different angles/ lengths in a diagram and one half of a line was labeled (8√2) and he needed to find the whole length of the line)

[lilfoo]

The steps the way he did it. if the equ is 8*SQR(2)*2

8*SQR(2)*2 = SQR(128 )*2 = SQR(128*4) [i think his error was here]= SQR(256*2) = SQR(512) = SQR(16^(2)*2) = 16*SQR(2)

Edit: i found the error

It was this step SQR(128 )+SQR(128 )=/=SQR(256)

EX:
2+2=4
=>SQR(4)+SQR(4)=4
=>SQR(8 )=/=4

[Kaylia]

so I work as a tutor and I have this one HS student who argues about EVERYTHING. He's a good kid, but that part drives me nuts. Anyways I am the English/HW club tutor and the math tutor/expert doesn't work on Wednesdays, and this kid had to do some algebra homework. Math had to be my least favorite subject in school, so I usually don't remember the stuff, I have to look it up to help the HS kids. So basically the student had to do this:

8√2 X 2

The owner and I couldn't quite remember how to do it so looked it up and found the easy way which is multiply the whole numbers then multiply the roots, giving the answer:

16√2

Peter has 8 "square root" and double this amount. How many squareroot does he have now?


You had the correct answer, and there isn't many way to do it.

[edit]
The only way to change what is inside a root (or exponant) is when both number have the same root/exponant

2* 8 * Sqrt(2)
Since Sqrt(4) = 2 and Sqrt(64)= 8
Sqrt(4) Sqrt(64) * Sqrt( 2)= Sqrt (512)

[Kaylia]

Also, make sure he understand the concept of equality, and that he is able to justify any "methods" he uses. In basic algebra, it's very important to use theorem and method you understand and can demonstrate. If you simply try to remember how to get to the solution, you're not doing maths, but simply playing with number. Won't do you any good.

[Charla]

Tomorrow, just tell him "well, because 8 is 2^3 and 2, naturally, is 2^1, that means we can represent the whole problem as (2^3)*(2^.5)*(2^1). And because multiplying with identical bases allows us to add the exponents, that means it's just 2^(3+.5+1), which is 2^4.5. Then tell him that this method is more useful later too, for finding derivatives involving e. With any luck, his impulse to use the more complicated way of solving stuff will work in your favor at that point. Or maybe he'll just get confused and ask you what e is (hint: it's somewhere between 2 and 3).

edit: am I just playing with numbers now?

[Ramor]

i think charla's way is great, it might be a bit complicated for him to understand that sqrt(2) is the same as 2^(one half), but i mean i was on my HS's math team and i guarantee that if you asked the entire team (freshman included) what something like 8^(2/3) was you'd get 90% of them saying 16, so i mean I suppose it depends on what he really understands and is able to comprehend,

but if he likes doing things the complicated way that's the way to tell him, it's complicated and it helps a hell of a lot later down the math track

[Kaylia]

Tomorrow, just tell him "well, because 8 is 2^3 and 2, naturally, is 2^1, that means we can represent the whole problem as (2^3)*(2^.5)*(2^1). And because multiplying with identical bases allows us to add the exponents, that means it's just 2^(3+.5+1), which is 2^4.5. Then tell him that this method is more useful later too, for finding derivatives involving e. With any luck, his impulse to use the more complicated way of solving stuff will work in your favor at that point. Or maybe he'll just get confused and ask you what e is (hint: it's somewhere between 2 and 3).

edit: am I just playing with numbers now?

Be careful or you will lost him tho. You need to actually make sure he understand what he is doing before confusing him with a more complex formalism.

[Jefe]

What "Charla" said, it's far easier to convert the sqrts() to their exponent counterparts (in your case ^1/2), then apply exponent rules/other applicable crazy rules to simplify them. Tell the kid to GTFO.

[Ksandra]

lol I'll stick to the other way Jaybar explained, no use teaching him extra stuff, if it was a kid who was eager to learn that's another story, but I deal with 10-14 kids a day helping them with homework, I don't have the time to sit down for 4 hours to teach him something he doesn't need yet, added to that he'll just argue all the way down.