Question 77785
<pre><font size = 5><b>
We are studying nth roots and rational exponents 
and I need help! 

Problem:

4/square root of 176 + 4/square root of 11=

{{{4/sqrt(176) + 4/sqrt(11)}}}

We begin by breaking 176 down into prime factors:

176 = 2x88 = 2x2x44 = 2x2x4x11 = 2x2x2x2x11

11 is already a prime number

So we have

{{{4/sqrt(2*2*2*2*11) + 4/sqrt(11)}}}

Group the like factors into pairs:

{{{4/sqrt((2*2)*(2*2)*11) + 4/sqrt(11)}}}

Write each pair as a square (of 2):

{{{4/sqrt((2^2)*(2^2)*(11)) + 4/sqrt(11)}}} 

Distribute the <font face = "symbol">Ö</font> over its factors:

{{{4/(sqrt(2^2)*sqrt(2^2)*sqrt(11)) + 4/sqrt(11)}}}

Now the square root of the square of a number is
just the number, so the square root of 2 squared is
just 2.

{{{4/(2*2*sqrt(11)) + 4/sqrt(11)}}}

Now the {{{2*2}}} on the bottom is just {{{4}}}

{{{4/(4*sqrt(11)) + 4/sqrt(11)}}}

Now we can cancel the {{{4}}}'s:

{{{1/sqrt(11) + 4/sqrt(11)}}}

Since the two fractions have a common
denominator, then we can just add the
two numerators and place it over the common
denominator:

{{{5/sqrt(11)}}}

If your teacher wants you to rationalize
the denominator and get the answer

{{{(5sqrt(11))/11}}}

then post again asking how to rationalize
the denominator.

Problem: How do you type in the square root of problems 
using symbols?

Take the example {{{sqrt(176)}}}

I'll have to tell you in steps, because if I type it on 
here like you are to type it in you will just show up as
{{{sqrt(176)}}}

1. Type three braces in a row { { { but don't skip a space
   between them as I did here. I skipped spaces between
   them here to keep the program from thinking I am
   starting a problem and giving an error message.
   These are open braces, not open parentheses. 
   The shifted key immediately to the right of the P key 
   on your keyboard gives open braces.
2. On the same line immediately after that type sqrt(176)
   That's parentheses, (shifted 9 and 0), not braces.
3. On the same line immediately after that type }}}
   Those are close braces, the shifted key just after the
   key which when shifted gives the open braces.
4. When you post your problem it will appear this way:{{{sqrt(176)}}}
 
Edwin</pre>