How to evaluate √2/3?

- Anguyennn

How to evaluate √2/3?

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- anonymous

is it \[\frac{ \sqrt{2} }{ 3 }\]

- Anguyennn

yes

- jackthegreatest

just think of it as \[\sqrt{2} \times \frac{ 1 }{ 3 }\]

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## More answers

- 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

are you sure?

- anonymous

Usually even upto 3 decimal digits is a good approximation if required

- Anguyennn

then what about 3/√3

- Anguyennn

how would you evaluate this?

- Anguyennn

|dw:1442687878850:dw|

- anonymous

\[\frac{3}{\sqrt{3}}=\frac{\sqrt{3}\sqrt{3}}{\sqrt{3}}=\sqrt{3} \approx 1.732\]

- anonymous

Notice that if you square 1.732, you get
\[(1.732)^2=2.999824 \neq 3\]

- anonymous

So it is only an approximation

- Anguyennn

but at the back of my answers it is showing √3 as the answer

- anonymous

|dw:1442698187908:dw|
\[\frac{ \sqrt{2} }{ 3 }=\frac{ 1.414 }{ 3 }=0.471 \approx\]

- 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

I know that you multiply the denominator by √3 and the numerator as well but how do you get the answer as √3?

- anonymous

\[\frac{3}{\sqrt{3}}=\frac{(\sqrt{3})^2}{\sqrt{3}}=(\sqrt{3})^{2-1}=(\sqrt{3})^{1}=\sqrt{3}\]

- anonymous

you simply cancel a factor of root 3

- Anguyennn

how did you get (√3)^2?

- 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

ohh ok

- Anguyennn

oh ok thank you i get it now thank you

- anonymous

You're welcome

- Anguyennn

could you help me with one more math problem?

- anonymous

sure

- Anguyennn

hello?

- Anguyennn

r u still there?

- anonymous

yep I'm here

- Anguyennn

##### 1 Attachment

- anonymous

Ok, show me your attempt or where you are having a problem

- Anguyennn

Like I know that you can simplify the 8 by doing √4x2

- Anguyennn

I just don't know how to do the cubed root

- 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

another example
|dw:1442690185880:dw|

- Anguyennn

ohh!!!

- Anguyennn

makes sense, but what about the second part because its a negative 27

- anonymous

That's slightly tricky!
|dw:1442690403700:dw|

- anonymous

@Anguyennn you there?

- anonymous

|dw:1442691246474:dw|

- 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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