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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,
$(99)^2=(100-1)^2$
$=(100)^2-2\times100\times1+(1)^2$
$=10000-200+1$
$= 9801$