Question

Find all real roots.

1.fourth roots of 625
2.fifth roots of -243
3.fourth roots of 256y^8

Answer 1

@wolf1728

Answer 2

\[625=5^4\]\[-243=(-6)^3\]\[256y^8=2^8y^8=(2y)^8\]GO....

Answer 3

(those are tips, not answers)

Answer 4

lol okay thankyou
hold on le tme try and finish it

Answer 5

sure.

Answer 6

for the first one would I raise both sides to the fourth power to cancel out the 5^4?

Answer 7

@SolomonZelman

Answer 8

YES.

Answer 9

I got a really large number..? I don't think that's right..?

Answer 10

\[\sqrt[4]{625}=\sqrt[4]{5^4}=5\]

Answer 11

Wasn't this what you meant?

Answer 12

oh yeah... sorry calculation error

Answer 13

\[\sqrt[5]{-243}=\sqrt[5]{(-3)^5}=?\]

Answer 14

\[\sqrt[4]{256y^8}=\sqrt[4]{4^4y^8}=4~\sqrt[4]{y^8}=4~\sqrt[4]{(y^2)~^4}=4y^2\]

Answer 15

Makes sense?

Answer 16

wait, sorry was the first one for #2 and the second one for #3?

Answer 17

but yeah it makes sense though

Answer 18

If you are familiar with logarithms, here is the first problem:
log(625) = 2.7958800173
Dividing that by 4 we get,
.69897
Get 10 and raise it to the .69897 power (or looking up the anti-log)
10^.69897
equals 5

Answer 19

I have no idea what logarithms are?

Answer 20

Okay, well that is how you would do that if you knew them.
I suppose if you have a math calculator you could solve it.
Does it have a key that reads y^x

Answer 21

it would, if I had my calculator with me at the moment...:l

Answer 22

Do you have Excel or OpenOffice on your computer?

Answer 23

yes I do

Answer 24

Very good. Well switch to that then in any cell enter =625^.25

Answer 25

entered

Answer 26

There should be an answer right in the same box

Answer 27

Press "Enter" or press the down arrow

Answer 28

I didn't get anything.. weirdly enough..

Answer 29

When you move out of the cell does anything remain in the cell?

Answer 30

If you know how to copy and paste copy this equation
=625^.25
paste it into any cell, then click Enter or press an arrow key

Answer 31

that's what I did and nothing happened.. but usually it does, I've used excel before.. idk what's going on.

Answer 32

It should work. I'm using Open Office and it works just fine. Excel works exactly the same.

Answer 33

nvm i think I got it

Answer 34

A five should appear in that cell right?

Answer 35

Yeah.

Answer 36

Okay - now you can use Excel instead of your calculator!

Answer 37

Yes I can. Thankyou! :)

Answer 38

We can move to the fifth root of -243 now.

Answer 39

ok

Answer 40

Even though Excel can help you, sometimes it might fail when you are looking for negative roots. When the exponent is even you get imaginary numbers but when it is odd, it is possible to get roots.
So, let's find the 5th root of 243 - that's right POSITIVE 243

Answer 41

If you are waiting for the formula it is
=243^.2
We are raising 243 to the 2/10 power which equals 1/5 - the fifth root.

Answer 42

no sorry I was trying to find the original problem. I found out it now ,but thanks

Answer 43

Anyway, try the fifth root of 243

Answer 44

243^.2

Answer 45

oops sorry wrong one I got 3

Answer 46

That is it - 3 is correct!

Answer 47

yaay! thanks

Answer 48

But remember we have to find the fifth root of -243, so the answer is actually -3.
To be sure multiply -3 5 times.
=-3*-3*-3*-3*-3

Answer 49

-243

Answer 50

Pretty good huh?

Answer 51

That leaves us with 4th root of 256y^8

Answer 52

mhm

Answer 53

We really don't need Excel for this.
256 = 16 * 16
and 16= 4 * 4
So the fourth root of 246 is 4
the 4th root of y^8 is ? (Do you know?)

Answer 54

Made a mistake in ABOVE problem - should be 256 for both numbers.

Answer 55

y^3?

Answer 56

y^3 =y^8?

Answer 57

no because if you multiply y^3 four time you'd get y^12

Answer 58

sorry I meant y^2

Answer 59

Yes y² is the answer.
Now for the entire answer the 4th root of 256y^8 is ?

Answer 60

4y^2

Answer 61

Yes !!! Very good

Answer 62

ThankYou!!! :)

Answer 63

If I as you a question and show you my work for it, Can you tell me what I did wrong please? If you're not busy.

Answer 64

*ask

Answer 65

Well okay sure.

Answer 66

for...\[\frac{ 6x }{ x+4 }=\frac{ 7x+4 }{ x+4 }\]
I Multipilied both sides by (x+4) to cancel out the denominators and got 6x=7x+4. Then I subtracted 7 on both sides and got -1x=4. Finally, I divied both sided by -1 and got x=-4.

Answer 67

What I would do is cross-multiply and get (x+4) / (x+4) = 7x + 4 / x+4
7x + 4 / x+4 = 1

Answer 68

but then wouldn't you multiply both sides by x+4 to cancel out the denominator?

Answer 69

I don't know. I guess that would give you
6x = 7x +4
Whereas I got 7x + 4 / 6x = 1
and I forgot to type in the 6 a little further back.
So far, I'd say we have the same equation.

Answer 70

did you get the same answer as me though?

Answer 71

Looking at your answer, for
6x = 7x +4
You can't subtract 7 from both sides
Is that where you get the -1 ?
6x -7 = -1?

Answer 72

hm we got the same answer...

Answer 73

But 6x -7 does not equal -1

Answer 74

I think my German Shepherd wants to go out for a walk - I might be gone for a while (15 minutes maybe)

Answer 75

oh yeah sorry, my brain's not thinking straight! & Lucky! You have a German Shepherd! alright i'll try to this on my own 'til them. :)

Answer 76

In case, I got to sleep by the time you comeback.. can you tell me what I did wrong in these.. I'll look over them tomorrow morning. @wolf1728

Answer 77

If $2000 is invested at 4% interest compounded monthly the value of the investment after t years is given by 2000(12.04/12) ^12t. What is the value of the investment after 3.5 years?...I actually didn't know how to do this problem at all.

Answer 78

\[\frac{ n^2-6n-27 }{ n^2-10n+9 }=\frac{ (n-9)(n+3) }{ (n-9)(n-1) }=\frac{ (n+3) }{ (n-1)}\] this is what I got, but I don't know what I did wrong same with the next one that's similar.

Answer 79

\[\frac{ 3n^3-36n^2+105n }{ 49n-7 }=\frac{ 3n(n^2-12n+35) }{ 7(7n-1) }=\frac{ 3n(n-7)(n-5) }{ 7(7n-1) }\]

Answer 80

I see that you are now offline, so I guess I'll work on this alone.
Looking again at this:
6x = 7x +4
Multiply both sides by 1/6
x = (7/6)x + 4/6
-(1/6) x = 4/6
-x = 4 OR
x = -4
Which works for 6x = 7x + 4
But when in the original equation
6x / (x+4) = 7x+4 / (x+4)
-4 produces division by zero.

Answer 81

Okay, I'm really good at compound interest.
$2,000.00 invested at 4% compounded monthly, value after 't' years is?
After 3.5 years?
The first thing to do is convert 4% compounded monthly to annual rate.
annual rate = ((1 + (.04/12))^12) -1
annual rate = .0407415429 or 4.07415429%

Present Value = principal * (1.0407415429)^years

Present Value = 2,000.00 * (1.0407415429)^years
For 3.5 years = 2,000.00 * (1.0407415429)^3.5
After 3.5 years = 2,000.00 * 1.1500060278
After 3.5 years = 2,300.01

Here's a good link for compound interest:
http://www.1728.org/compint.htm

Answer 82

n²−6n−27
n²−10n+9

(n−9)(n+3)(n−9)(n−1)=(n+3)(n−1)

Well I looked at this one and the other one but I didn't find anything wrong with either. I hope the compound interest answer helps you out.