Sandy asks…
how do you divide fractions with a radical?
such as (1/2) divided by √3/2, the answer i see is √ 3/3 but idont know how to get it
admin answers:
1/2 divided by √3/2 is the same as
1/2 multiplied by 2/√3 which equals 1/√3
u multiply 1/√3 by √3/√3 because u can't have a root as a denominator
the answer would be √3/(√3*√3)=√3/3
Lizzie asks…
How to divide a fraction by a fraction with radicals?
Please explain what I do and why. Don't just show your work with an answer. For example, in the problem (1/2) ÷ (√3/2)
What would the first step be and why?
Would I multiply by the reciprocal?
EX:
(1/2)∙(2√3)= 2/2√3 ? And if so how would I solve this from there?
I have also heard that the first step is to multiply the whole problem by the conjugate. If so what is the conjugate and how do I do this? If incorrect what should ?I do?
Will vote best answer. I am looking to understand how to solve all problems with fractions and radicals, not this particular problem. I'm just using it as an example. So if you just solve it and don't explain, it's pretty much useless for me. Thanks.
Does it make a difference if you multiply by the conjugate first versus reciprocal? If so, how? Also can a final answer have a radical in the denominator. I have heard yes and no. Why or why not?
admin answers:
(1/2) / (√3/2) --- Problem Stated
(2/1)* (1/2) / (√3/2) * (2/1) --- Multiplied each side by 2/1 (reciprocal)
1 / (√3/1) --- Simplified multiplication
(1/√3) --- Simplified √3/1 to √3
(1/√3) * (√3/√3) = (1√3)/3 --- Simplified further to get the √ out of the Denominator
= √3/3. --- Simplified 1 * √3 to get final solution
Edit:
"Also can a final answer have a radical in the denominator"
Yes a final answer can have a radical in the denominator, though if this is for school I'm almost positive your teachers will make you move it to the top as its not considered completely simplified.
Ruth asks…
How to divide this radicals?
2√6
------
4√5
The dashed line is a fraction/ division symbol. We are suppose to reduce them completely and with no decimals. I'm completely clueless with this paper and I need a little help! Thank you so, so, so much!
admin answers:
We need to rationalize the denominator.
No radicals in denominator so..
It is a fraction so to get rid of the radical in denom multiply by sqrt(5) in both numerator and denom.
Result is 2 sqrt(30)/ ((4)(5))
reduce the 2 and 4 by 2
sqrt(30)/10
Donald asks…
Trouble Dividing Radicals?
I am trying to do the problem "The square root of 15 divided by 3 times the square root of 80 in fraction form it is square root of 15 / 3*square root of 80. After attempting to look up how to divide radicals on the internet, i came up with the answer 5*sq. root of 3/50. Is this correct? If not, could someone link me a good source to learn about this, or explain where i might have gone wrong?
admin answers:
(√15)/(3√80) = (1/3)√(15/80) = (1/3)√(3/16) = (1/3)(√3)/(√16) = (1/3)(1/4)√3 = (1/12)√3
Chris asks…
How To Divide Radical Expressions?
I DO NOT need confusing answers. Please. Help me out---include rules and easy-to-follow examples. I will be choosing the best answer!
Now, I know how to simplify this:
8(roots)6
------------
2(roots)3 = 4(roots)2
And the like. As long as they divide evenly into each other, I'm good.
What I get confused on is when the denominators are larger than the numerators, or they don't go into the numerators easily, etc.. Such as:
9(roots)3
------------
(roots)5 = ? (I'm thinking the answer is 9(roots)3/5, but why? Explain this.)
Also:
(roots)40
------------
(roots)90 = ? (Do you simplify this to:
(roots)4
----------
(roots)9
and solve it from there...
...or do you simplify it to:
2/3
by simply dividing each number by 10?)
I got 2/3 because (root)40 turns to 2(root)10, and (roots)90 turns to 3(root)10, and when divided this equals 2/3...or so I got.
And then there's this:
16
----------
(roots)8 = ? Would it be 8(root)2? By finding the factors of 8, and getting (root)2 x (root)4, which would turn to 2(root)2, and then you would divide 16 and 2, and get 8(roots)2?
Basically, I really need to know this:
Do you simplify first? Like (root)40 over (root)90 would be (root)4/9? And would you simplify (root)4/9 to 2/3 from there? And like (root)2 over (root)6? Would that turn to (root)1/3, or (root)2/6, or what?
Or do you NOT simplify like you usually would with fractions, and simply get the factors of (root)40 and (root)90, and work it from there?
Please, tell me how to do this!
PLEASE.
admin answers:
Either way works, and all of your answers seem correct except the
16
----------
(roots)8
one. (I'll explain that one in a minute.) For example,
(root)1/3
is the same as
(root)2/6.
In any problem, you can feel free to simplify a root before dividing, or you can divide first and then simplify, or any combination of the above.
As for
16
----------
(roots)8
you must first simplify the denominator to become 2(root)2. Then you can divide out the 2 to get
8
----------
(root)2
From here, you can either leave the answer as is or recall that
1
----------
(root)2
=
(root)2
----------
2
This would simplify the above expression to
8(root)2
----------
2
or
4(root)2.
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