Find the squares of the following numbers by visual method:
(i) 52
(ii) 95
(iii) 505
(iv) 702
(v) 99.

To find: 

We have to find the squares of the given numbers by visual method.

Solution:

We know that,

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

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

(i)

$52$ can be written as,

$=50+2$

Therefore,

$(52)^2=(50+2)^2$

$=(50)^2+2\times50\times2+(2)^2$

$=2500+200+4$

$= 2704$   

(ii) 

$95$ can be written as,

$=100-5$

Therefore,

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

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

$=10000-1000+25$

$= 9025$   

(iii) 

$505$ can be written as,

$=500+5$

Therefore,

$(505)^2=(500+5)^2$

$=(500)^2+2\times500\times5+(5)^2$

$=250000+5000+25$

$= 255025$   

(iv) 

$702$ can be written as,

$=700+2$

Therefore,

$(702)^2=(700+2)^2$

$=(700)^2+2\times700\times2+(2)^2$

$=490000+2800+4$

$= 492804$    

(v) 

$99$ can be written as,

$=100-1$

Therefore,

$(99)^2=(100-1)^2$

$=(100)^2-2\times100\times1+(1)^2$

$=10000-200+1$

$= 9801$     

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Updated on: 10-Oct-2022

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