Anguyennn
  • Anguyennn
How to evaluate √2/3?
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
is it \[\frac{ \sqrt{2} }{ 3 }\]
Anguyennn
  • Anguyennn
yes
jackthegreatest
  • jackthegreatest
just think of it as \[\sqrt{2} \times \frac{ 1 }{ 3 }\]

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anonymous
  • anonymous
It's an irrational number, it cannot be evaluated, you can only approximate it, \[\sqrt{2} \approx 1.4142\] so we have \[\frac{\sqrt{2}}{3} \approx \frac{1.414}{3}=0.471333....\]
Anguyennn
  • Anguyennn
are you sure?
anonymous
  • anonymous
Usually even upto 3 decimal digits is a good approximation if required
Anguyennn
  • Anguyennn
then what about 3/√3
Anguyennn
  • Anguyennn
how would you evaluate this?
Anguyennn
  • Anguyennn
|dw:1442687878850:dw|
anonymous
  • anonymous
\[\frac{3}{\sqrt{3}}=\frac{\sqrt{3}\sqrt{3}}{\sqrt{3}}=\sqrt{3} \approx 1.732\]
anonymous
  • anonymous
Notice that if you square 1.732, you get \[(1.732)^2=2.999824 \neq 3\]
anonymous
  • anonymous
So it is only an approximation
Anguyennn
  • Anguyennn
but at the back of my answers it is showing √3 as the answer
anonymous
  • anonymous
|dw:1442698187908:dw| \[\frac{ \sqrt{2} }{ 3 }=\frac{ 1.414 }{ 3 }=0.471 \approx\]
anonymous
  • anonymous
That is the exactl answer, \[\sqrt{3}\] is the exact answer \[1.732\] is an approximation, if someone asks what is the answer you'd say \[\sqrt{3}\] but if you for example need a value, you can use an approximate value
Anguyennn
  • Anguyennn
I know that you multiply the denominator by √3 and the numerator as well but how do you get the answer as √3?
anonymous
  • anonymous
\[\frac{3}{\sqrt{3}}=\frac{(\sqrt{3})^2}{\sqrt{3}}=(\sqrt{3})^{2-1}=(\sqrt{3})^{1}=\sqrt{3}\]
anonymous
  • anonymous
you simply cancel a factor of root 3
Anguyennn
  • Anguyennn
how did you get (√3)^2?
anonymous
  • anonymous
3 can be thought of the square of square root of 3, just like how you can write for example 10 as 2 times 5, I've written 3 as root 3 times root 3, or square of root 3 \[3=\sqrt{3} \times \sqrt{3}=\sqrt{9}=(\sqrt{3})^2\]
Anguyennn
  • Anguyennn
ohh ok
Anguyennn
  • Anguyennn
oh ok thank you i get it now thank you
anonymous
  • anonymous
You're welcome
Anguyennn
  • Anguyennn
could you help me with one more math problem?
anonymous
  • anonymous
sure
Anguyennn
  • Anguyennn
hello?
Anguyennn
  • Anguyennn
r u still there?
anonymous
  • anonymous
yep I'm here
Anguyennn
  • Anguyennn
anonymous
  • anonymous
Ok, show me your attempt or where you are having a problem
Anguyennn
  • Anguyennn
Like I know that you can simplify the 8 by doing √4x2
Anguyennn
  • Anguyennn
I just don't know how to do the cubed root
anonymous
  • anonymous
Ok, let's see Suppose I have |dw:1442689623211:dw| The number outside the radical, which tell which root you have to find, you have to pair up factors that many times inside a root to take them out For example |dw:1442689712453:dw||dw:1442689797599:dw| Now let's suppose a slightly more difficult example |dw:1442689856316:dw|
anonymous
  • anonymous
another example |dw:1442690185880:dw|
Anguyennn
  • Anguyennn
ohh!!!
Anguyennn
  • Anguyennn
makes sense, but what about the second part because its a negative 27
anonymous
  • anonymous
That's slightly tricky! |dw:1442690403700:dw|
anonymous
  • anonymous
@Anguyennn you there?
anonymous
  • anonymous
|dw:1442691246474:dw|
Anguyennn
  • Anguyennn
hello? i am so sorry the computer was frozen and i did not know how to get back to it until now. i apologize

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