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

To find: 

We have to find the squares of the given numbers.

Solution:

We know that,

$(a+b)^2=a^2+2ab+b^2$

(i) $425$ can be written as,

$=400+25$

Therefore,

$(425)^2=(400+25)^2$

$=(400)^2+2\times400\times25+(25)^2$

$=160000+20000+625$

$=   180625$ 

(ii) $575$ can be written as,

$=500+75$

Therefore,

$(575)^2=(500+75)^2$

$=(500)^2+2\times500\times75+(75)^2$

$=250000+75000+5625$

$=   330625$ 

(iii) $405$ can be written as,

$=400+5$

Therefore,

$(405)^2=(400+5)^2$

$=(400)^2+2\times400\times5+(5)^2$

$=160000+4000+25$

$=   164025$  

(iv) $205$ can be written as,

$=200+5$

Therefore,

$(205)^2=(200+5)^2$

$=(200)^2+2\times200\times5+(5)^2$

$=40000+2000+25$

$=   42025$   

(v) $95$ can be written as,

$=100-5$

Therefore,

$(95)^2=(100-5)^2$

$=(100)^2-2\times100\times5+(5)^2$

$=10000-1000+25$

$=   9025$   

(vi) $745$ can be written as,

$=700+45$

Therefore,

$(745)^2=(700+45)^2$

$=(700)^2+2\times700\times45+(45)^2$

$=490000+63000+2025$

$=   555025$    

(vii) $512$ can be written as,

$=500+12$

Therefore,

$(512)^2=(500+12)^2$

$=(500)^2+2\times500\times12+(12)^2$

$=250000+12000+144$

$=   262144$  

(viii) $995$ can be written as,

$=1000-5$

Therefore,

$(995)^2=(1000-5)^2$

$=(1000)^2-2\times1000\times5+(5)^2$

$=1000000-10000+25$

$=    990025$

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Updated on: 10-Oct-2022

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