Unit Digit of $1001^{2} + 1002^{2}$

$1^2+2^2=5$ ................[answer]

as,the unit digit of this two number is very small and summation of their square(unit digit) is less than 10,so we can do it in this way.

• Unit digit of $1001^2 = \color{#20A900}{1}$
• Unit digit of $1002^2 = \color{#20A900}{4}$

$\text{Sum} = {\color{#20A900}{1 + 4}} = {\color{#20A900}{\boxed{5}}}$

The end of the first number is 1^2 =1 and the second number is 2^2=4.1+4=5.

• $1001^2 = 1002001$

• $1002^2 = 1004004$

$1002001+1004004 = 200600\color{#20A900}5$

The unit digit is $\color{#20A900}\boxed{5}$