Find the square of the following …

Ncert solutions Grade 8 Mathematics Science Chapters in NCERT Solutions - Mathematics , Class 8 Exercises in Squares and Square Roots Question 1 Q1) Find the square of the following numbers. (i) 32 (ii) 35 (iii) 86 (iv) 93 (v) 71 (vi) 46 Solution Transcript Solution: (i) \left(32\right)^2=\left(30+2\right)^2=\left(30\right)^2+2\times30\times2+\left(2\right)^2(32) 2 =(30+2) 2 =(30) 2 +2×30×2+(2) 2 [\because\left(a+b\right)^2=a^2+2ab+b^2∵(a+b) 2 =a 2 +2ab+b 2 ] = 900 + 120 + 4 = 1024 (ii) \left(35\right)^2=\left(30+5\right)^2=\left(30\right)^2+2\times30\times5+\left(5\right)^2(35) 2 =(30+5) 2 =(30) 2 +2×30×5+(5) 2 [\because\left(a+b\right)^2=a^2+2ab+b^2∵(a+b) 2 =a 2 +2ab+b 2 = 900 + 300 + 25 = 1225 (iii) \left(86\right)^2=\left(80+6\right)^2=\left(80\right)^2+2\times80\times6+\left(6\right)^2(86) 2 =(80+6) 2 =(80) 2 +2×80×6+(6) 2 [\because\left(a+b\right)^2=a^2+2ab+b^2∵(a+b) 2 =a 2 +2ab+b 2 = 8100 + 540 + 9 = 8649 (iv) \left(93\right)^2=\left(90+3\right)^2=\left(90\right)^2+2\times90\times3+\left(3\right)^2(93) 2 =(90+3) 2 =(90) 2 +2×90×3+(3) 2 [\because\left(a+b\right)^2=a^2+2ab+b^2∵(a+b) 2 =a 2 +2ab+b 2 ] = 8100 + 540 + 9 = 8649 (v) \left(71\right)^2=\left(70+1\right)^2=\left(70\right)^2+2\times70\times1+\left(1\right)^2(71) 2 =(70+1) 2 =(70) 2 +2×70×1+(1) 2 [\because\left(a+b\right)^2=a^2+2ab+b^2∵(a+b) 2 =a 2 +2ab+b 2 = 4900 + 140 + 1 = 5041 (vi) \left(46\right)^2=\left(40+6\right)^2=\left(40\right)^2+2\times40\times6+\left(6\right)^2(46) 2 =(40+6) 2 =(40) 2 +2×40×6+(6) 2 [\because\left(a+b\right)^2=a^2+2ab+b^2∵(a+b) 2 =a 2 +2ab+b 2 ] = 1600 + 480 + 36 = 2116