We are given :
[tex] \sqrt{4x^{2}-20x+25} [/tex]
Step 1: factor the part inside square root
The function given inside square root is of quadratic form.
So let us try to factorise it using AC method.
Here A*C = 4*25 = 100
so we have to find factors of 100 that add up to give -20.
the two factors are -10 and -10.
Rewriting the function :
[tex] 4x^{2} -20x+25 [/tex]
=[tex] 4x^{2} -10x-10x+25 [/tex]
=[tex] 2x(2x-5) - 5(2x-5) [/tex]
=[tex] (2x-5)^{2} [/tex]
Step 2:
Now we take square root of the factorised form
[tex] \sqrt{(2x-5)^2} [/tex]
= [tex] 2x-5 [/tex]
Answer : (2x-5)
