Question

Find the square of the following numbers using suitable properties :
1. 562
2.671

Answer 1

$\huge \tt\green {\underbrace{Answer}}$

Square of 562 - 315844

Square of 671- 450241

Answer 2

Answer:

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Step-by-step explanation:

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