Question

Algebra 2 help (attachment)

Answer 1

Can someone walk me through one or 2 problems?

Answer 2

Hmm, it's basically rewriting the equations in a different way.

Answer 3

For example the 3rd equation

Answer 4

okay

Answer 5

for some reason i can't use the equation button anymore, it worked before

Answer 6

okay just tell me in words maybe?

Answer 7

ok

Answer 8

can you break the number 27 down to it's prime factors?

Answer 9

27
/\
3 x 9
/\
3 x 3

Answer 10

indeed

Answer 11

so you agree with me that the cube root of 27 can also be written as (3^3)^(1/3) (sorry for the format, i hope you understand

Answer 12

basically the cube root of 3 to the power of three (or in other words, just 3)

Answer 13

is the 1/3 the exponent?

Answer 14

yes

Answer 15

okay

Answer 16

1/3 in the exponent is the same as the cube root (it's a different way of writing a root)

Answer 17

so can i just write 3 as cubed not 1/3 ?

Answer 18

hmm, i guess yes if i understand the question correctly

Answer 19

(3^3)^3

Answer 20

for example, square root of 4 is the same as 4^1/2 and the cube root of 4 is 4^1/3... etc.

Answer 21

so can i just say (3^3)^3 ?

Answer 22

no, that's a much bigger number.

Answer 23

oh ok

Answer 24

so how did u get 1/3 from the problem

Answer 25

it's the cube root of (3^3)

Answer 26

I know how you got 3^3, but idk how you got 1/3

Answer 27

how did you know that..

Answer 28

you see that image?

Answer 29

yes okay I see it

Answer 30

so what do I do next

Answer 31

I made a second picture, hope that clears things up

Answer 32

Okay thank you!

Answer 33

The steps are clear then?

Answer 34

Shall i do the 4th as well or do you think you can solve the others on your own?

Answer 35

wait so what would be the answer to the 3rd one?

Answer 36

the square root of 3 can't be simplyfied, so it's smply 3 times the square root of 3 (the 3 comes from the cube root of 27)

Answer 37

so it's (3^3)^1/3

Answer 38

that's the cube root of 27

Answer 39

which results in 3. but you also have the square root of 3.

Answer 40

Which means, the end result is SQRT(3) * 3

Answer 41

Roots of prime numbers can't be simplyfied

Answer 42

okay let's do 4

Answer 43

So you always break the numbers under the root down to their prime factors, then simplify, it's usually the easiest method

Answer 44

Okay hold on then

Answer 45

Right, so in equation 4, you have two cube roots. The cube root of 45 and the cube root of 75. It would be easier to just multiply 45 and 75 and take the cube root of the result. (it'll give the same answer)

Answer 46

that way you'll only need to do it once.

Answer 47

45
/ \
5 9
/ / \
5 3 3

Answer 48

i got 15

Answer 49

Correct, you figured that out quite fast

Answer 50

okay, what do I do next

Answer 51

What did you do to arrive at 15?

Answer 52

45 x 75 and cube root

Answer 53

You did the cube root of 45*75 from the top of your head or did you use a calculator for it?

Answer 54

calculator lol i wouldnt be able to do that in my head

Answer 55

alright, i wouldn't either, but i still can with some simple steps and i'm sure you can too. let me show you.

Answer 56

no that's okay! but thanks

Answer 57

so is that the answer?

Answer 58

15?

Answer 59

Yes 15 is the end result.

Answer 60

If you take 45 and 75 and break them both up in their prime factorials

Answer 61

can we also do numbers 7 and 8?

Answer 62

you'll get 5*3*3*5*5*3

Answer 63

sure

Answer 64

but do you see now why it's 15?

Answer 65

yes!

Answer 66

Alight, let's see if you can do the same in the next question then

Answer 67

oh 7 is a different type let me see

Answer 68

you can't really do anything with the x, so that will just stay as it is, so the only thing you'd have to do is simplify the square root of 36 and multiply the outcome of that with the square root of x^3

Answer 69

6x3

Answer 70

where did you get the 3 from?

Answer 71

6x^3 *

Answer 72

oh right, yes.

Answer 73

except

Answer 74

the x is still under the root

Answer 75

the 6 isn't, of course.

Answer 76

so to be clear 6*SQRT(x^3)

Answer 77

yes

Answer 78

what about 8?

Answer 79

Same story, x and y can't be simplified, so only the cube root of 125 can be simplyfied, the x and y stay exactly as they are (including the root)

Answer 80

cube root of 125 can easily be done from your head as well, if you use prime factors like i explained before.

Answer 81

5

Answer 82

Yes

Answer 83

5y^2z^4

Answer 84

ye except you forgot the root once again ;)

Answer 85

square root over the whole asnwer?

Answer 86

answer*

Answer 87

no, cube root over y and z, but not the 5.

Answer 88

the 5 is the result of 'freeing' the 125 from the cube root. But since it's unknown what y and z are exactly, they are stuck under the root, they can't be 'freed' so they stay in root prison so to speak.

Answer 89

oh okk! what about 9? last one if u have time

Answer 90

Sure. that one is important to understand as well

Answer 91

Obviously, you don't know what k is, so you can't simplify k itself, but you can still write it in another way because

Answer 92

remember how i said a square root can be written as "to the power of one half" ?

Answer 93

so basically you have the square root of 18, times k to the power of 6 halves.

Answer 94

does that make sense or should i paint it?