Question

What is the exact value of the expression the square root 72. − the square root of 8. + the square root of 128.? Simplify if possible.

8the square root of 2.
12the square root of 2.
8the square root of 3.
12the square root of 3.
I got C. Is that correct?

Answer 1

@.Sam. (rip amy)

Answer 2

\[\large\rm \sqrt{72}-\color{orangered}{\sqrt8}+\sqrt{128}\]With these types of problems, I would recommend that you start by trying to simplify the smallest number first. If it doesn't simplify, then chances are all of the other roots will probably be some multiple of that one.

Answer 3

\(\large\rm \sqrt{8}=\sqrt{4\cdot2}=\sqrt{4}\cdot\sqrt2\)
8 contains a perfect square, so it looks like, yes, we will be able to simplify this one a bit.

Answer 4

Square root of 4 is 2, so we have \(\large\rm \sqrt{8}=2\sqrt2\)
Which makes our expression look like this,\[\large\rm \sqrt{72}-\color{orangered}{2\sqrt2}+\sqrt{128}\]

Answer 5

So what you should expect is that the other two roots will PROBABLY simplify to square root 2's as well.

Answer 6

So try to do the same for the 72.
You'll probably be left with a 2 under the root,
that should help you figure it out.

Answer 7

You can divide all of them by 8 so, 9 and 8 and 16 and 8.

Answer 8

I got it wrong putting C but I am retaking it. Its B correct? 12 and 2?

Answer 9

If you want to leave the middle term as sqrt8,
then yes, you can break down the other numbers the way you specified,
\(\large\rm \sqrt{9\cdot8}-\sqrt8+\sqrt{16\cdot8}\)
Which becomes,
\(\large\rm 3\sqrt8-\sqrt8+4\sqrt8\)
Combining like-terms shows us that we have a total of 6 of these square root 8's.
\(\large\rm 6\sqrt8\)

And from before, we figured that sqrt8 is 2sqrt2,
\(\large\rm 6\cdot2\sqrt2\)

So yes, B sounds correct :) Good job

Answer 10

Thanks :D