Question

What is: 20x+25 " alt=" \sqrt{4x^{2} -20x+25 " align="absmiddle" class="latex-formula">

Answer 1

We are given :

$\sqrt{4x^{2}-20x+25}$

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 :

$4x^{2} -20x+25$

=$4x^{2} -10x-10x+25$

=$2x(2x-5) - 5(2x-5)$

=$(2x-5)^{2}$

Step 2:

Now we take square root of the factorised form

$\sqrt{(2x-5)^2}$

= $2x-5$

Answer : (2x-5)