Question 916193
<pre>
{{{2sqrt(72)+3sqrt(50)-sqrt(128)}}}

Think of square numbers other than 1 which are

1. factors of 72. They are 4, 9, 36. The largest is 36
2. factors of 50. There is only one, 25.
3  factors of 128. They are 4, 8, and 64.  The largest is 64

Rewrite each as a product of two numbers one of which is the
largest possible square number

{{{2sqrt(36*2)+3sqrt(25*2)-sqrt(64*2)}}}

Write each as the product of two square roots:

{{{2sqrt(36)sqrt(2)+3sqrt(25)sqrt(2)-sqrt(64)sqrt(2))}}}

Take the square roots of the square numbers:

{{{2*6sqrt(2)+3*5sqrt(2)-8sqrt(2)}}}

{{{12sqrt(2)+15sqrt(2)-8sqrt(2)}}}

They are like terms, just like {{{12x+15x-8x=19x}}}

Answer:  {{{19sqrt(2)}}}

Edwin</pre>