How to evaluate √2/3?

- Anguyennn

How to evaluate √2/3?

- katieb

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this

and **thousands** of other questions

- anonymous

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

- Anguyennn

yes

- jackthegreatest

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

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## 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

Looking for something else?

Not the answer you are looking for? Search for more explanations.