Melody

I am not sure what the right word is

but yes they can be used to cancel each other out. 

Like + and -

Or

× and ÷

I'm not explaining this very well. :/

Everyone does it MG.  I think I do it more than most others.

I just think you need to on guard for this type of error the same as I do :)

$$\\ (\sqrt{x})^5=(x^{1/2})^5=x^{5/2}=x^{2.5}$$

There is nothing else that you can do :)

@@ End of Day Wrap   Sat 6/6/15   Sydney, Australia Time   12:15am (yes, it is Sun morn   )   ♪ ♫

A good day to you all,

Today our great answers were provided by TitaniumRome, MathsGod1, CPhill, Awesomeee, Eloise1st, asinus, Alan, Civonamzuk, radix and steva.   Thanks everyone.   

Not really Eloise.

$$\sqrt{\frac{1}{3}}$$    is an irrational number.  

That means that you can not write it as a fraction with ordinary digits.

You can not write it exactly as a decimal either so I think this is the answer that is wanted

$$\sqrt{\frac{1}{3}}=\frac{1}{\sqrt3}$$

and it is usual to rationalize the denominator so this can be written as 

$$\sqrt{\frac{1}{3}}=\frac{1}{\sqrt3}=\frac{1}{\sqrt3}\times \frac{\sqrt3}{\sqrt3}=\frac{\sqrt3}{3}$$

Eloise1st   I have added your post to our "Reference Material" sticky thread.   Thanks you :))

Sun 7/6/15

If you would like to comment on other site issues please do so on the Lantern Thread.  Thank you.    

Interest Posts: 

FTJ means 'For the juniors' 

You should be able to do some of this yourself.

What is x? what is y?   So what does x+y represent?

What is S? what is T?   So what dioes S+T represent?

Now think about what x*S would represent

and

what does y*T reptresent?

Now you can say waht x*S + y*T  would represent.

Give it a go !!

Here is another question for you MathsGod :))

$$3+8\div16\times(8+5)$$

(It might help if you remember that a division sign is the same as a fraction line)

Do you know about order of operation?  Maybe you call it PEDMAS or BODMAS or BEDMAS ?

I'll remind you / teach you  anyway :)

When doing a question like this there are strict rules about the order you have to do it in.

Most counties seem to call it     PEDMAS

1) Parentheses (they are brackets )   

2) Exponents  (they are powers)

3) Dividsion and multiplication are EQUALLY important.  Do them from left to right.

4) Addition and subtraction are EQUALLY important.  Do them from left to right.

Now use this order  to answer the question.  Use LaTex please :))

When I use LaTex I almost always copy the line of just done and then past it underneath, then I just change it a little and I keep going down the page like this.  Maybe you already do this :))

Ok MathsGod, lets look at what you have done :)

Ok I can see the problem.

Perhaps you have a very slight problem with dyslexia MG.

This is probably not the right word and every suffers from what I am talking about a little bit, I know I do.

But I do think you need to be extra careful.  You have swapped the digits over AGAIN.

This time you did it when you put the numbers into the calculator. 

So your calculations are perfect        (except that you copied my orriginal question down wrong)

It is your calculator answer that is incorrect!

ALSO I would have prefered that you finished it like this (plus you did not put your equal signs in )

$$\\=\frac{91}{2}\times\frac{7}{17}\times\frac{1}{3}\\\\
=\frac{91\times7\times 1}{2\times17\times 3}\\\\
=\frac{637}{34\times 3}\\\\
=\frac{637}{102}\\\\
=6\frac{25}{102}$$

You can take as many steps as you want but it is better if it is all kept together :)