study the sign of the function inside the square root and exclude the interval which the function is negative since the square root of negative is undefined in Real numbers

for example square root of ( x^2 - 9 )

study x^2 - 9 sign

first find the root of it

(x-3 )( x+3 ) = 0 so x = - 3 and +3

now take numbers less than -3 and between -3 and 3, and bigger than 3 sub it in x^2 - 9

take -4, 1 , 4

-4 give us (-4)^2 - 9 = 7 > 0 positive so any number less than -3 will give us positive

1 , 1^2 - 9 < 0 so any number between -3 and 3 will give us negative

4 will give us positive now

the domain of square root of ( x^2 - 9 ) will be all real numbers except the numbers between -3 and 3

your book said that because we want the intervals where (4-x)^2 - 5 positive

(4-x)^2 - 5 >= 0

(4-x)^2 >= 5

l 4 - x l >= square 5

you should know that