Question 490372

it is a number {{{25}}} which is a square number of {{{5}}}, and the sum of{{{ 9}}} and {{{16}}} is {{{25}}}

 {{{9}}} and {{{16}}} are also square numbers of {{{3}}} and {{{4}}}

so, {{{3^2+4^2=5^2}}} or {{{9+16=25}}}

-two square numbers numbers whose sum is {{{100}}}

number {{{100}}} could be written as a sum of {{{36}}} and {{{64}}}
both of these numbers could be written as a square numbers {{{6^2}}} and {{{8^2}}}

so, {{{6^2+8^2 = 100 }}}


{{{sqrt(100) = 10}}}; {{{sqrt(1000)= 31.6}}}, so largest square less than {{{1000 }}}is {{{31^2}}}
Between {{{100}}} and {{{1000}}} there are {{{31-10 = 21}}} square numbers (22 if 100 itself is included since 100 = 102)