Question

Find the squares of the following numbers
(i) 425 (ii) 575
(iii) 405 (iv) 205
(v) 95 (vi) 745
(vii) 512 (viii) 995

Answer 1

(i) $(425{)}^2$
Here n = 42
$\therefore n(n+1)=42(42+1)42\times 43=1806$
$\therefore (425{)}^2=180625$

(ii) $(575{)}^2$
Here n = 57
$\therefore n(n+1)=57(57+1)57\times 58=3306$
$\therefore (575{)}^2=330625$

(iii) $(405{)}^2$
Here n = 40
$\therefore n(n+1)=40(40+1)40\times 41=1640$
$\therefore (405{)}^2=164025$

(iv) $(205{)}^2$
Here n = 20
$\therefore n(n+1)=20(20+1)20\times 21=420$
$\therefore (205{)}^2=42025$

(v) $(95{)}^2$
Here n = 9
$\therefore n(n+1)=9(9+1)=9\times 10=90$
$\therefore (95{)}^2=9025$

(vi) $(745{)}^2$
Here n = 74
$\therefore n(n+1)=74(74+1)=74\times 75=5550$
$\therefore (745{)}^2=555025$

(vii) $(512{)}^2$
Here a= 1, b= 2
$\therefore (5ab{)}^2=(250+ab)\times 1000+(ab{)}^2$
$\therefore (512{)}^2=(250+12)\times 1000+(12{)}^2$
$=262\times 1000+144$
$=262000+144=262144$

(viii) $(995{)}^2$
Here n =99
$\therefore n(n+1)=99(99+1)=99\times 100=9900$
$\therefore (995{)}^2=990025$