Question

Can you check my answer?
Nakim simplified 3√2x + x√8x - 5√18x and got the answer -10√2x
Part 1:Using complete sentences, explain what Nakim did wrong.

Part 2: Show all your work to simplify the expression.

Show all your work to simplify the expression.

My response was:
3√2x cannot be simplified any further.
x√8x = x√2*2*2x = 2x√2x
-5√18x = -5√3*3*2x = -5*3√x = -15√x


Combine like terms
3√2x + 2x√2x = 5√2x
- 15√x = -15√x

So my answer is 5√2x - 15√x

Answer 1

like terms are 3√2x and - 15√x

Answer 2

2x√2x remains as it is

Answer 3

also, -5√18x is not simplified properly.

Answer 4

-5√18x = -5√3*3*2x
correct till here.

Answer 5

-5√18x = -5√3*3*2x = -5*3 *√2x
right ?

Answer 6

you said
My response was:
3√2x cannot be simplified any further. <--- true
x√8x = x√2*2*2x = 2x√2x <------------true
-5√18x = -5√3*3*2x = -5*3√x = -15√x <--- you lost a 2 that should be -15 sqrt(2x)

Answer 7

@haileemackk you there ?

Answer 8

Sorry, I had to leave after I posted this and I left my computer on.
Even when I combined 3√2x + 2x√2x - 15√2x = -10√2x
I still got -10√2x

But if 2x√2x is on it's own, does that mean the answer is
3√2x - 15√2x = -12√2x + 2x√2x?

Answer 9

maybe you see what is going on this way.
factor out \( \sqrt{2x} \) from each term to get
\[ (3 -15 + 2x) \sqrt{2x} \]
or
\[ (2x -12) \sqrt{2x} \]
you cannot simplify 2x+12. we could factor out a 2 and write it as
\[ (x-12) 2 \sqrt{2x} \]
or we can write it as you did
\[ 2x \sqrt{2x} -12 \sqrt{2x} \]
any of those are ok, and any might show up as an answer in a multiple choice.

Answer 10

** \[ (x-6) 2 \sqrt{2x} \]
typo on one of the versions

Answer 11

When you factored it out, I understood much better! Thank you so much!