Question

Nakim simplified 3 times the square root of 2x plus x times the square root of 8x minus 5 times the square root of 18x and got -10x times the square root of 2x for an answer.

Part 1: Using complete sentences, explain what Nakim did wrong.

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

Answer 1

\[3\sqrt{2x} + x \sqrt{8x} - 5 \sqrt{18x} and got -10x \sqrt{2x}\] what did he do wrong?

Answer 2

First: in all the terms, we need the number under the radical to be the same.
√2x is the radical in the first term. Nothing to do there.
√8x is the second radical. But 8 = 4*2, so we can write it as √8x = √4*2x = √4 * √2x = 2√2x.
Now, what do you get for the third one?

Answer 3

To be honest, I'm not good at these at all.

Answer 4

I'm trying to understand what you just said. @Nory

Answer 5

It's okay. I didn't explain it very well.

Answer 6

So to add radicals, you have to get the same number under the radical sign in all the terms. Does that make any sense?

Answer 7

Yes.

Answer 8

But that is not the case in your problem...yet.
We have to get the same number under the radical in all the terms. We can do this by finding a square number to factor out of the stuff under the radical.
Ex. √4x well, we can just factor out the four...
√4x = √4 * √x = 2√x
Does that make sense? Maybe that's where you're getting stuck.

Answer 9

Yes, that does make sense.

Answer 10

Okay. Now we can do the same thing to our radicals.
Let's work on x√8x. We can basically use the same technique as above.
x√8x = x√4*2x = x√4 * √2x = 2x√2x
Does that make sense?

Answer 11

I see what you did there. I understand that part.

Answer 12

Okay, good.
Now 5√18x = 5√9 * √2x = 15√2x.
That makes sense, right?
Now write all our terms out in a line.
3√2x + 2x√2x - 15√2x. Does this look familiar?

Answer 13

do you mean, \[10 \sqrt{18x}\] ?

Answer 14

\[5\sqrt{9} * \sqrt{2}\]

Answer 15

Go on...that √9 looks like it could be simplified.

Answer 16

\[10\sqrt{3}\] ?

Answer 17

@Nory

Answer 18

I think I see where you got mixed up...
5√9 * √2 = 5*3 *√2 = 15√2

Answer 19

Oh okay.

Answer 20

Now you can add/subtract them as you would regular numbers.

Answer 21

What about the 3 and the 2x?

Answer 22

What 3?
The 2x under the radical, you just tack on at the end. For example, to do 2√x + 5√x, you first do 2+5=7, then add the x. √7x.

Answer 23

\[3\sqrt{2x} + 2x \sqrt{2x} - 15\sqrt{2x}\] You said it was this?

Answer 24

Yeah, that looks like what we got. Go on...?

Answer 25

\[5\sqrt{5x}\] I don't know..

Answer 26

You add the 3 and the 15, then the 2x. The 2x can't be added to the 3 and the 15 because it has an x in it.
So"-12√2x + 2√2x. Do you see how I got that?

Answer 27

[Sorry--this is kind of a long, intensive math session...]

Answer 28

I think you mixed it up. where did you get the \[2\sqrt{2x}\] ?

Answer 29

Oops: 2x√2x. Thanks for catching my mistake.

Answer 30

What would be the next step?

Answer 31

There is no next step. There's nothing left to add, so you're done.

Answer 32

\[-12\sqrt{2x}\] + \[2x \sqrt{2x}\] well for this problem, I have to find out what the person did wrong.

Answer 33

I actually did the problem the way he did it the first time, and then I realized my mistake.
What he did was he added the -12√2x and the 2x√2x, and you can't do that because the 2x√2x has an x in it (in front of the radical). It's like adding 2 and 5x^2: you can't do that, can you?

Answer 34

Alright, thank you for all this information!(:

Answer 35

Good work. And thanks for staying with me all this time. What was this, like an hour? :)

Answer 36

Haha, 34 minutes :P