Question

Find the exact value of the radical expression in simplest form.
the square root of 4 times y cubed − the square root of y cubed

Answer 1

\[\sqrt{4y^3}-\sqrt{y^3}\]

Answer 2

@Compassionate

Answer 3

What is the square root of 4? 2. \[2\sqrt{y^3} - \sqrt{y^3}\]

Now, you see we have y to the 3. What this really means is \[\sqrt{y * y * y}\]

So, I'm sure you learned that this equals. \[2y \sqrt{y} - y \sqrt{y}\]

Now, notice the radicals are the same thus, we can subtract them from each other. \[2y - y + \sqrt{y} - \sqrt{y} = y\]

Answer 4

Oh, thanks!

Answer 5

Was that helpful? Do you understand what I did?

Answer 6

Yes, It took me a second to understand that last part,but I'm pretty sure I get it.

Answer 7

So, it's just \[\sqrt{y}\]

Answer 8

All I did on the last part was sorta rearange the terms to make you see what I'm doing.

No, it's just y.

Answer 9

Let's be sure.

Answer 10

You see, I had \[2y \sqrt{y} - y \sqrt{y}\]
In order to subtract radicals, I need to make the radicals equal. So you see I have y under both the radical bars. So I subtract the radical from the radicals, and the outside terms from the outside. That is. 2y from y and y from y, which gives me just y.

Answer 11

What happened to the sqrt y ??

Answer 12

It got subtracted.

Answer 13

I subtracted square root of y from the square root of y, and 2y from y. Which just gives me y. We're subtracting the entire left side from the right.

Answer 14

Ohhh, I get it.

Answer 15

Let's see what radar has to say. I may be wrong.