kathyworld09
1.) [4^3 sqrt. a] + [^3 sqrt. 64a]
2.) [sqrt. 5] - [7 sqrt. 80] + [4 sqrt. 45]
Delete
Share
This Question is Closed
siddharth_tiwari
Best Response
You've already chosen the best response.
0
u guyz ought to help everyone.......plz help me also.......
polpak
Best Response
You've already chosen the best response.
0
If you can convert the bit under the radical into a product of some squares you can pull out the square and you might end up with something you can combine with addition/subtraction.
polpak
Best Response
You've already chosen the best response.
0
Sidd, please stop stalking me.
a933793
Best Response
You've already chosen the best response.
0
2) -15 Sqrt[5]
not exactly what the first is asking though
kathyworld09
Best Response
You've already chosen the best response.
0
siddharth tiwari : ....... well i need help with these so ? ......
polpak
Best Response
You've already chosen the best response.
0
a933793: please don't just give people answers. If they want the solution there's wolfram alpha. If they want to learn it'll take more explanation than what you've provided.
siddharth_tiwari
Best Response
You've already chosen the best response.
0
k..........just got anxious...u kno....when u dont have any way out to do the quesn ,,,,how does it feels.......well dont mind sir....was just a request not an order.....sry if it mean here
polpak
Best Response
You've already chosen the best response.
0
Kathy, can you factor out some of the product under the sqrt and make it into a product (multiplication) of some squared factors?
kathyworld09
Best Response
You've already chosen the best response.
0
i have no idea polopak , i get so confused with these sqrts :/
polpak
Best Response
You've already chosen the best response.
0
Don't worry about the square roots for now. Can you factor 80?
kathyworld09
Best Response
You've already chosen the best response.
0
well the common gcf of all 5, 80, 45 is 5
kathyworld09
Best Response
You've already chosen the best response.
0
for problem 2
polpak
Best Response
You've already chosen the best response.
0
Not greatest common factor, Just rewrite them as a product of their factors.
\(80 = 8 *10 = (4*2) * (5*2) \)
\(= (2*2*2)*(5*2) = (2*2)*(2*2) * 5\)
\(= 2^2 * 2^2 * 5\)
polpak
Best Response
You've already chosen the best response.
0
Now try doing the same thing for 45.
polpak
Best Response
You've already chosen the best response.
0
And be sure to group up any squares you find
kathyworld09
Best Response
You've already chosen the best response.
0
1,5,9,45 = factors for 45
polpak
Best Response
You've already chosen the best response.
0
Ignore 1 and itself.
kathyworld09
Best Response
You've already chosen the best response.
0
and for 5 , it would be just 5
polpak
Best Response
You've already chosen the best response.
0
45 = 9*5, and 9 is what?
kathyworld09
Best Response
You've already chosen the best response.
0
3*3
polpak
Best Response
You've already chosen the best response.
0
\(3^2\)
polpak
Best Response
You've already chosen the best response.
0
Ok, so lets rewrite the problem now with the squares..
\(\sqrt{5} - 7\sqrt{2^2 * 2^2 * 5} + 4\sqrt{3^2 * 5}\)
polpak
Best Response
You've already chosen the best response.
0
Now any square factor we can pull out of the square root by removing the square.
polpak
Best Response
You've already chosen the best response.
0
\(7*\sqrt{2^2 * 2^2 * 5} = 7 * \sqrt{2^2} * \sqrt{2^2} * \sqrt{5} = ?\)
kathyworld09
Best Response
You've already chosen the best response.
0
i multiply the sqrts ?
polpak
Best Response
You've already chosen the best response.
0
No, take the square root of the squared term. What is \(\sqrt{2^2}\)
polpak
Best Response
You've already chosen the best response.
0
If a >= 0, then \(\sqrt{a^2} = a\)
polpak
Best Response
You've already chosen the best response.
0
Are you still with me?
kathyworld09
Best Response
You've already chosen the best response.
0
yes
polpak
Best Response
You've already chosen the best response.
0
Ok, great. So what's \(\sqrt{2^2}\)
kathyworld09
Best Response
You've already chosen the best response.
0
sqrt. 4
polpak
Best Response
You've already chosen the best response.
0
Yes, but what's sqrt of 4? It's 2 right? You don't need to evaluate \(2^2\) because when you take the square root you just take off the square and the square root. They undo eachother.
\(\sqrt{2^2} = 2. \)
\(\sqrt{3^3} = 3.\)
etc.
polpak
Best Response
You've already chosen the best response.
0
Err
\(\sqrt{3^2} = 3\)
kathyworld09
Best Response
You've already chosen the best response.
0
so it would just be 2 and 3 ?
polpak
Best Response
You've already chosen the best response.
0
Not quite.
So we have
\(7*\sqrt{80} = 7*\sqrt{2^2 *2^2 * 5} = 7*\sqrt{2^2}*\sqrt{2^2} * \sqrt{5} =?\)
kathyworld09
Best Response
You've already chosen the best response.
0
7 * 2 sqrt. 5 ?
kathyworld09
Best Response
You've already chosen the best response.
0
correction : 7 * 2 * 2 * sqrt. 5 ?
polpak
Best Response
You've already chosen the best response.
0
Right. So now simplify that
polpak
Best Response
You've already chosen the best response.
0
7*2*2 = ?
kathyworld09
Best Response
You've already chosen the best response.
0
becuase their are 2 [sqrt.2^2]
polpak
Best Response
You've already chosen the best response.
0
No, we got rid of the square root already on those.
\((7*2*2)\sqrt{5} \)
\(= (14*2 ) \sqrt{5}\)
\(= 28 \sqrt{5}\)
kathyworld09
Best Response
You've already chosen the best response.
0
can we still simplfy that ?
polpak
Best Response
You've already chosen the best response.
0
No, but we have \(\sqrt{5} - 28\sqrt{5} + 4\sqrt{45}\)
So if we can get the \(4\sqrt{45}\) to be a multiple of \(\sqrt{5}\) we can combine them all.
polpak
Best Response
You've already chosen the best response.
0
So lets look at \(\sqrt{45}\).
We said that that was 45 = 9*5 = \(3^2*5\), so what would \(4*\sqrt{45}\) simplify to?
kathyworld09
Best Response
You've already chosen the best response.
0
2 sqrt. 5 ?
kathyworld09
Best Response
You've already chosen the best response.
0
4 sqrt . 5 *3^2
polpak
Best Response
You've already chosen the best response.
0
So what is the next step now that you have that?
polpak
Best Response
You've already chosen the best response.
0
Just like the last one, we pull out each squared factor.
kathyworld09
Best Response
You've already chosen the best response.
0
4*3 sqrt.5 ?
polpak
Best Response
You've already chosen the best response.
0
Yes. Which is?
polpak
Best Response
You've already chosen the best response.
0
What's 4*3?
kathyworld09
Best Response
You've already chosen the best response.
0
12 sqrt. 5
polpak
Best Response
You've already chosen the best response.
0
Right. So now we have \(1\sqrt{5} - 28\sqrt{5} + 12\sqrt{5}\)
kathyworld09
Best Response
You've already chosen the best response.
0
-15 sqrt. 5 ?
polpak
Best Response
You've already chosen the best response.
0
Yes.
kathyworld09
Best Response
You've already chosen the best response.
0
and for the 1st problem , i factor out which is a ?
polpak
Best Response
You've already chosen the best response.
0
Do the same thing. Factor everything under the square root. Pull out any square factors by removing the square, leave the rest under the square root. Then combine.
polpak
Best Response
You've already chosen the best response.
0
Go ahead and do it yourself, step by step and I'll point out when/if you get off track.
polpak
Best Response
You've already chosen the best response.
0
Just post each step as you go.
polpak
Best Response
You've already chosen the best response.
0
What's the first step?
kathyworld09
Best Response
You've already chosen the best response.
0
[4^3 sqrt. a] + [^3 sqrt. 64a] : what do i do with the powers before the sqrt ?
kathyworld09
Best Response
You've already chosen the best response.
0
are you still here ?
polpak
Best Response
You've already chosen the best response.
0
I don't understand.. Do you have cube roots?
\(4\sqrt[3]{a} + \sqrt[3]{64a}\)
If so then instead of squares, you're looking for cubes.
\(\sqrt[3]{2^3} = 2 \) is an example you will probably find useful.
If you are still working on this, give it a try and write out your steps and where you're stuck and I'll check back again later.
kathyworld09
Best Response
You've already chosen the best response.
0
yes i still need help please
kathyworld09
Best Response
You've already chosen the best response.
0
polpak: i think it'll result to 16\[^{3} \sqrt{a}\]
polpak
Best Response
You've already chosen the best response.
0
What was the first step you did?