Question 45930
<pre><font size = 5 color = "purple"><b>add or subtract as indicated 
  _     ___
2<font face = "symbol">Ö</font>5 + 5<font face = "symbol">Ö</font>125

You can't break 5 down because it's prime, but you can 
break down 125 into primes

125 = 5·25 = 5·5·5, so substitute 5·5·5 for 125
  _     _____
2<font face = "symbol">Ö</font>5 + 5<font face = "symbol">Ö</font>5·5·5

Since it's a square root we group like factors into 
twos. (If it were a cube root you would group into 
threes)

  _     ________
2<font face = "symbol">Ö</font>5 + 5<font face = "symbol">Ö</font>(5·5)·5
 
Since (5·5) is the same as 5², so we can substitute
5² for (5·5) 
        ____
2V5 + 5<font face = "symbol">Ö</font>5²·5

Now we can take individual square roots of the factors
under the second radical
  _     __  _
2<font face = "symbol">Ö</font>5 + 5<font face = "symbol">Ö</font>5²·<font face = "symbol">Ö</font>5

Taking the square root of '5 squared' just takes 
away the square and the radical, and you just have 5:
  _        _
2<font face = "symbol">Ö</font>5 + 5·5·<font face = "symbol">Ö</font>5
  _      _ 
2<font face = "symbol">Ö</font>5 + 25<font face = "symbol">Ö</font>5
                            _
Now you can factor out the <font face = "symbol">Ö</font>5
 _
<font face = "symbol">Ö</font>5(2 + 25)

2 plus 25 is 27
 _
<font face = "symbol">Ö</font>5(27)

Write the 27 first
   _
27<font face = "symbol">Ö</font>5

Edwin</pre>