Find the squares of the following numbers:
(i) 127
(ii) 503
(iii) 451
(iv) 862
(v) 265.

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) $127$ can be written as,

$127=120+7$

Therefore,

$(127)^2=(120+7)^2$

$=(120)^2+2\times120\times7+7^2$

$=14400+1680+49$

$=16129$

(ii) $503$ can be written as,

$503=500+3$

Therefore,

$(503)^2=(500+3)^2$

$=(500)^2+2\times500\times3+3^2$

$=250000+3000+9$

$=253009$ 

(iii) $451$ can be written as,

$451=400+51$

Therefore,

$(451)^2=(400+51)^2$

$=(400)^2+2\times400\times51+(51)^2$

$=160000+40800+2601$

$=203401$  

(iv) $862$ can be written as,

$862=800+62$

Therefore,

$(862)^2=(800+62)^2$

$=(800)^2+2\times800\times62+(62)^2$

$=640000+99200+3844$

$=   743044$

(v) $265$ can be written as,

$265=200+65$

Therefore,

$(265)^2=(200+65)^2$

$=(200)^2+2\times200\times65+(65)^2$

$=40000+26000+4225$

$=   70225$

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Updated on: 10-Oct-2022

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