Maths help, hard surd

For
sqrt(9 - 4*sqrt(5))
Note that
9 = 5 + 4
and see if you can complete the square for the sqrt(5) term.

uhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

Try, its a hard question, so try and work through some ideas.
You know what completing the square is?

sqrt(9 - 4*sqrt(5))
The first thing to note is that 9 = 4+5, so this equals
sqrt(5 - 4*sqrt(5) + 4)
Note the way I've swapped terms around. Can you complete the square?

i dont see why we need to complete the square, if i get it to something like (x+1)^2 the square root and square cancel out then its basic surds

That is exactly the reason for doing it.

so its (2-root5)^2

Other way round and the square and root cancel as you say so
sqrt(5)-2

cheers ok, but why cant it be 2-root5

What is that value?

so its (2-root5)^2
Ok so i did that with trail and error, how do i actually factorise it

(a+b)^2 = 5 - 2*2*sqrt(5) + 4
Factorize by completing the square with a = sqrt(5) as it must square to 5, and the correction term outside the square will be 0. Or just spot a=sqrt(5), b=-2.

the negative version..