Question

Can the expression s sqrt(3) + 27 sqrt(2^5) + 9 sqrt(3s) be simplified into an expression with fewer terms? Explain and simplify, if possible.

Answer 1

I know it simplifies to s sqrt(3) + 3s^2 sqrt(3s) + 9 sqrt(3s)
can it be simplified to fewer terms? How and why?

Answer 2

This is the original expression? :o
\[\Large s \sqrt3+27\sqrt{2^5}+9\sqrt{3s}\]

Answer 3

Yes it is

Answer 4

All three terms contain different degrees of s, so no we can't combine them any further. At least not without doing some fancy factoring business :d\[\Large \color{royalblue}{s^1} \sqrt3+\color{royalblue}{s^0}27\sqrt{2^5}+\color{royalblue}{s^{1/2}}9\sqrt{3}\]

s^1/2 = sqrt s
s^0 = 1,
i just wanted to throw those in to show that they're different D:

Answer 5

So what is the final answer? I'm confused, sorry

Answer 6

`Can the expression be simplified into an expression with fewer terms?`
No.

`Explain and simplify, if possible.`
Simplification not possible.
I hope my explanation helped a tiny bit :C I'm not sure exactly how to explain it.

Answer 7

Like do you understand why `these` three terms can't be combined together?\[\Large x^2+x+1\]They're different degrees of x, so they don't combine, yes? :o
Where as something like:\[\Large x^2+2x^2+1\]Would simplify to:\[\Large 3x^2+1\]Since the squared terms can be combined.

Answer 8

Your problem is the same idea, the degrees on s are just not as clearly written out.

Answer 9

So once it's simplified to \[s \sqrt{3} + 27^{2}\sqrt{2} + 9\sqrt{3s}\] that's as far as it goes?

Answer 10

Yeah, I now understand the degree thing!

Answer 11

Wait! I know that thing was incorrect!

Answer 12

ya I'm not sure what happened there :) lol
your middle term kinda magically changed to something else!

Answer 13

i know :/ haha okay so once I get here I can't go any further?
s sqrt(3) + 3s^2 sqrt(3s) + 9 sqrt(3s)
even though the two last terms have the same degree of s?

Answer 14

Hmm I don't understand what's going on, your middle term keeps changing :(\[\Large s \sqrt3+\color{red}{27\sqrt{2^5}}+9\sqrt{3s}\]Is that red term correct?
Or is the 2 supposed to be an `s` or something?

Answer 15

\[\sqrt{27s ^{5}}\] This is the correct one... I'm not wearing my glasses and I'm tired (not the best mix)

Answer 16

lol :)

Answer 17

\[\Large s \sqrt3+\sqrt{27s^5}+9\sqrt{3s}\]Oh ok I see what you did there,\[\Large s \sqrt3+3s^2\sqrt{3s}+9\sqrt{3s}\]

Answer 18

So I guess you're looking at it and thinking "Hey! they both have a sqrt(3s), can't we combine them??"

But you want to look at the `entire` s value within each term.
If I move things around, just a smidge! ...\[\Large s \sqrt3+3\sqrt3\color{royalblue}{s^2\sqrt{s}}+9\sqrt3\color{orangered}{\sqrt{s}}\]Can you see how the s's are quite different between the second and third term?

Answer 19

Wouldn't it just stay outside of the radical?

Answer 20

hmm? :o

Answer 21

You could factor a sqrt(s) out of each term, yes.\[\Large \sqrt s\left(3\sqrt3 s^2+9\sqrt3\right)\]But I don't think that's what they had in mind when they asked you to `combine` them.

Answer 22

You can't directly add them.

Answer 23

I just got it! It can't be a like term if the coefficients aren't the same!

Answer 24

The coefficients? D: ehh we don't really care about those :x
It's all about the `s`'s!! :D

Answer 25

Yeah but if the radicals are the same, it doesn't matter because the coefficients are not... They are not like terms and so I can't add them together.

Answer 26

Ok ok ok :)
I just want to make sure we agree on what a `coefficient` is.
coefficient refers to the number in front of the variable.

So if we had:\[\Large 5x+3x\]We `can` combine these terms despise the fact that the coefficients are different.\[\Large 8x\]
What's stopping us from combining our `s`'s is that they are not like terms (as you said), different exponent on each variable.
Just in case there was any confusion on that. c: