question_answer 1)

Find the square of the following numbers: (i) 32                                      (ii) 35                                     (iii) 86                                    (iv) 93 (v) 71                     (vi) 46

Answer:

                (i) 32 \[32=30+2\] Therefore, \[{{32}^{2}}={{(30+2)}^{2}}\] \[=30(30+2)+2(30+2)\] \[=900+60+60+4\] = 1024 (ii) 35 \[35=30+5\] Therefore, \[{{35}^{2}}={{(30+2)}^{2}}\] \[=30\left( 30+5 \right)+5\left( 30+5 \right)\] \[=900+150+150+25\] = 1225 (iii) 86 \[86=80+6\] Therefore, \[{{86}^{2}}={{\left( 80+6 \right)}^{2}}\] \[=80(80+6)+6(80+6)\] \[=6400+480+480+36\] = 7396 (iv) 93 \[93=90+3\] Therefore, \[{{93}^{2}}={{(90+3)}^{2}}\] \[=90(90+3)+3(90+3)\] \[=8100+270+270+9\] = 8649 (v) 71 \[71=70+1\] Therefore, \[{{71}^{2}}={{(70+1)}^{2}}\] \[=70(70+1)+1(70+1)\] \[=4900+70+70+1\] = 5041 (vi) 46 \[46=40+6\] Therefore, \[{{46}^{2}}={{(40+6)}^{2}}\] \[=40(40+6)+6(40+6)\] \[=1600+240+240+36\] = 2116.