Question

can the square root of 130 be simplified.

Answer 1

$No,\ because\ 130=2\cdot5\cdot13.\\\\\sqrt{130}\ is\ irrational\ number,\ cannot\ be\ simplified.$

Answer 2

 now were going to factor out 130, and according to that principle, any numeral needs a pair to be pulled to the outside of the radical. 

130 breaks down to 10 x 13 
13 is prime so leave it, 10 breaks down to 5 x 2. 
We have 13 x 5 x 2 and no pairs. Sqr root of 130 is already as simplified as possible. Use a calculator for an approximation. 11.40