Question

Anyone good at radicals? I need help pleaseeeeee

Answer 1

What do you need help with, specifically?

Answer 2

\[3\sqrt{5}-2\sqrt{7}+\sqrt{45}-\sqrt{28}\]

Answer 3

What is the question? Do you need to find an approximation, or do you need to represent it in fractional powers, etc...

Answer 4

blow me

Answer 5

It is asking me to simplify the equation

Answer 6

ok.
pay attention to these pairs: 3*root(5) wtih root(45)
and 2root(7) and root(28)
There's a way to simplify this problem into 2 terms.

Answer 7

\[\sqrt{9}\sqrt{5}\] Think about what these terms can be simplified into...
you could easily take the root of 9, or you could multiply 9 and five under the radical.

Answer 8

Ok well i know the square root of 9 is 3!

Answer 9

I don't think there is one fore 5 :o

Answer 10

So...
\[3\sqrt{5} = \sqrt{9}\sqrt{5} = \sqrt{45}\]
You see?
you can do the same thing with the other terms. Pay attention to the sign (plus or neg) as well. these won't cancel.

Answer 11

Now i understand what to do! but do i simplify further?

Answer 12

yes. once the numbers under the radicals are the same, you can add or subtract like terms
Ex: \[3\sqrt{3} + 2\sqrt{3} = 5\sqrt{3}\]
etc...

Answer 13

because my answer choices are
a. \[2\sqrt{12}\]
b.\[2\sqrt{2}\]
c.6\[6\sqrt{5}-4\sqrt{7}\]
d.\[6\sqrt{10}-4\sqrt{14}\]

Answer 14

Yes. One of them is definitely correct.
You need to simplify those radicals as far as you can.

Answer 15

If you're still confused about what to do, let me know what's confusing.

Answer 16

Well im trying to see how i can simplify them because 3root5 can not be simplified because nothing goes in them unless it's 1

Answer 17

then 9root5 would be 3root5 because nothing goes in to 5

Answer 18

No. It has a pair. remember?
\[3\sqrt{5} = \sqrt{45}\]

Answer 19

so am i simplifying \[3\sqrt{5}=\sqrt{45}\]?

Answer 20

so, let's look at the original problem. I'll take you through it.

Answer 21

\[3\sqrt{5} - 2\sqrt{7} + \sqrt{45} - \sqrt{28}\]
Now recognize that the first and third terms are the same:
\[\sqrt{45} =\sqrt{9*5} = \sqrt{9}\sqrt{5} = 3\sqrt{5}\]

Answer 22

So since they're both positive, your equation should now look like this:
\[3\sqrt{5} - 2\sqrt{7} + 3\sqrt{5} - \sqrt{28}\]
now you can add the like terms, and it should look like this:
\[6\sqrt{5} - 2\sqrt{7} - \sqrt{28}\]

Answer 23

Now we can do the same thing with the last two terms.
Well we have \[2\sqrt{7} \] and \[\sqrt{28}\]
if you noticed the pattern...
\[\sqrt{28} = \sqrt{7*4} = \sqrt{4}\sqrt{7} = 2\sqrt{7}\]
so now the equation should look like;
\[6\sqrt{5} - 2\sqrt{7} -2\sqrt{7}\]
Do you see how to get there now?
There's one more simplification to do...

Answer 24

Yes i think so! now you subtact the terms correct?

Answer 25

so outside the radical, would it be 2?

Answer 26

yes!
and a -2(x) - 2x will equal -4x.
but instead of x you have root(7)

Answer 27

is the answer b? :)

Answer 28

can you help me with a few more?

Answer 29

no...
That's not correct.

Answer 30

wait no! a

Answer 31

My mistake.

Answer 32

Nope :(
let me put it a different way.
if you had this problem, how would you solve it?
\[3x -2x +3x-2x\]

Answer 33

you would subtract the like terms. so 3x-2x would be 1 then the other 3x-2x would also be 1. then add 1+ 1 together and the answer would be 2x?

Answer 34

hello?

Answer 35

sorry.
I should've said brb.

Answer 36

No i'ts alright :)

Answer 37

yes.
The problem you have is essentially like this:
3x−2y+3x−2y

Answer 38

so, like you just did, but now they don't all combine.

Answer 39

Thats where im getting confused. would i add the x's with the x terms? and the y terms with the y terms?

Answer 40

exactly

Answer 41

so 3x+3x is 6

Answer 42

and 2y + 2y is 4

Answer 43

But now... i can't add 6x + 4y correct?

Answer 44

yes, but remember that they're negative. so it's -4y

Answer 45

and no, you can't add them. They have different variables

Answer 46

ok so now where do i go from there?

Answer 47

well, that's it!
the final answer is 6x -4y
except
x = \[\sqrt{5}\]

and

y = \[\sqrt{7}\]

and in this way, radicals act like variables. you can't add them.

Answer 48

I really hope I'm helping...

Answer 49

Yes you are! thank you so much, you taught me the step by step process and made it easier for me :) can you help me with a different radical problem ?

Answer 50

Sure. Go ahead.

Answer 51

\[\sqrt{5}(8+3\sqrt{6})\]

Answer 52

well, to start, you can distribute the root(5)

Answer 53

what would that give you?

Answer 54

it would be square root of 40

Answer 55

no, the whole equation. type it all out. remember to distribute the root(5) to both terms.

Answer 56

I want to make sure you're getting the steps correct.

Answer 57

oh ok you want me to work out the problem to see if im understanding it. Ok one sec

Answer 58

Ok wait a minute. I just relooked at the problem dont i have to add \[\sqrt{5} + \sqrt{6}\] together? because i got 11, then i added 8+3 together and i also got 11

Answer 59

nope.
here, think of it this way:
y(8 + 3x)

Answer 60

you can't add the 8 and three together.

Answer 61

you would get 8y + 3xy, right?

Answer 62

right

Answer 63

do you see where this is going?

Answer 64

yes so far, but how am i distributing sq root of 5? i thought i was supposed to be multiplying \[\sqrt{5}(8\] first before i go farther into the problem

Answer 65

so with \[\sqrt{5}(8 + 3\sqrt{6})\]
imagine for the purposes of distribution that root(5) is a variable and so is root(6), they can't be added. that's like saying 3*4 = 3+4. It doesn't work.
But, they can be multiplied.

Answer 66

so yes, start with root(5) * 8 and then root(5) *3* root(6)

Answer 67

Ok so (5)*8 is 40 then

Answer 68

no

Answer 69

Huh?

Answer 70

Oh wait

Answer 71

Hold on

Answer 72

do i have to find the sq root for 8?

Answer 73

no, treat it like a variable. You don't know root(8), so you just say,
\[8\sqrt{5}\]

Answer 74

5 is in the radical, not 8. You just need to group them for now.

Answer 75

it's not tough, just like y(8 + 3x) = 8y + 3xy

Answer 76

just distribute root(5) to both terms like the "y"

Answer 77

Ohhh ok let me see

Answer 78

so, i wrote down the problem and i distributed 5 to 8 which is 40 then 5 to 3 which is 15

Answer 79

Now im trying to see if i add 40 + 15 together?

Answer 80

I dont think i do though because i still have the sq root 6 in my problem

Answer 81

You should've gotten this:
\[8\sqrt{5} + 3\sqrt{6}\sqrt{5}\]

Answer 82

the 5 and 8 CANNOT be multiplied directly. One acts like a variable.
Let me put it this way: root 5 = 2.236067977.....
so if you were to ACTUALLY multiply 8 * root(5), you would get some crazy irrational number like 17.88854382....

So instead, we just keep it as root(5). Think of it this way, you have 8 packs of root(5).

Answer 83

Oh i see. My mistake, i see where you're going with it but now to simplify that would it be \[8\sqrt{5}+3\sqrt{30}\] ?

Answer 84

YES!

Answer 85

now just simplify 3*root(30) one step further...

Answer 86

You think you've got it now?

Answer 87

Yes i do :) but 30 is not a perfect sq? would it be 130?

Answer 88

or 10?

Answer 89

hrm? no
Actually, my mistake, there is no further simplification...

Answer 90

That should be the final answer.
I hope I helped...

Answer 91

Hahaha i was wondering what was going on! and yes yes you did :) i was able to figure out the answer right? you were BIG help :)