Question

In how many ways 1105 can be expresses as the sum of two squares of natural number ?

• A. 1
• B. 2
• C. 3
• D. 4
• E. None of these

Answer 1

The correct option is C 3

It is given that,

" The sum of squares of two numbers is $1105.$ "

The possible numbers which gives the result $1105$ after adding their squares are,

$\Rightarrow$ $32$ and $9$

${32}^2+9^2=1024+81=1105$

$\Rightarrow$ $31$ and $12$

${31}^2+{12}^2=961+144=1105$

$\Rightarrow$ $24$ and $23$

${24}^2+{23}^2=576+529=1105$

$\therefore$ There are $3$ ways $1105$ can be written as the sum of the squares of two natural numbers.