Question

(1) Is there a general method to compute the squares of numbers like
15.25, 3...? Explain it using algebra.
(2) Given below is a method to calculate 372?
9 x 100
900
32= 9
42 x 10
420
2 x (3 x 7) = 42
72
49
1369
372
i) Check this for some more two-digit numbers.
ü) Explain why this is correct, using algebra.
iii) Find an easy method to compute squares of number
ending in 5.
(3)
Look at this pattern
12 + (4 x 2)
32
22 + (4 x3)
42
32 + (4 x 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.
(5) Prove that for any natural number ending in 3, its square ends in 9.
What about numbers ending in 5? And numbers ending in 4?​

Answer 1

Answer:

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