Q3 of 95 Page 74

Look at this pattern

12 + (4 × 2) = 32


22 + (4 × 3) = 42


32 + (4 × 4) = 52


i) Write the next two lines.


ii) Explain the general principle using algebra.

i) 42 + (4×5) = 62

52 + (4×6) = 72


ii) General principle,


By observing the pattern we can write a general line as:


x2 + (4× (x+1)) = ( x+2 )2


Now, let us prove this using algebra.


x2 + ( 4× (x+1)) = x2 + 4x + 4


(x+2)2 = x2 + 4x + 4 ……using , (x+y)2 = x2 + 2xy + y2


Cleary, both these terms are equal.


Hence, proved.


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2

Given below is a method to calculate 372?


Find an easy method to compute squares of number ending in 5.

 2

Given below is a method to calculate 372?


Find an easy method to compute squares of number ending in 5.

 3

Look at this pattern

12 + (4 × 2) = 32


22 + (4 × 3) = 42


32 + (4 × 4) = 52


i) Write the next two lines.


ii) Explain the general principle using algebra.

 4

Explain using algebra, the fact that the square of any natural number which is not a multiple of 3, leaves remainder 1 on division by 3.