Question

if k is a positive integer between 0 and 60 what is one possible value of k for which Square root(k+7)-5 is a posstive integer?

Answer 1

k=23. 23+7=30 , 30-5 = 25 , the square root of 25 is 5, a positive integer

Answer 2

think of the roots we know that are integers
sqrt{1^2},sqrt{2^2},sqrt{3^2}.....
so first lets worry about the sqrt{k+7}
we know that this cant be <= 5 because we know sqrt{k+7}-5 must be greater than 0
so
we remove 1,2,3,4,5 as options for the answer of sqrt{k+7}
so we start with 6
sqrt{36}=6 so sqrt{29+7} = 6
sqrt{49} = 7 so sqrt{42+7}=7
sqrt {64}=sqrt{57+7}=8 and
sqrt{81} = sqrt{74+7}=9
74>60
so possible values for k are 29,42,57