How is the equation $x_1+5x_2-\sqrt{(2x_3)} = 1$ a linear equation? The answer given in the book is, "The Equation is linear".
How can an equation involving a square root like the above equation be a linear equation?
here is the cutting of the book,

How is the equation $x_1+5x_2-\sqrt{(2x_3)} = 1$ a linear equation? The answer given in the book is, "The Equation is linear".
How can an equation involving a square root like the above equation be a linear equation?
here is the cutting of the book,

Answer to title question: It's NOT!
Your question is legitimate:
$$x_1+5x_2-\sqrt{2x_3\;} = 1\tag{1}$$
$(1)$ is not a linear equation as you suggest.
Nor is $(f)$ linear, as typeset in the image.
I suspect there was a misprint in the problem set (book), or a careless typo that the author (and/or editor) over-looked, and which was intended to be:
$$x_1 + 5x_2 - \sqrt{2}\;\cdot x_3 = 1\tag{2}$$
NOW, $(2)$ is a linear equation.
Here is the real exercise found on Amazon...

$$(x+5y-1)=\sqrt{2z}$$ so $$(x+5y-1)^2=2z$$ and this is not a linear equation because the order of variabes are 2.