Question

ENT-2021-2
MARKS : 25
TIME 1 HOUR
MATHEMATICS

)
1 The vene ol squaring is called
2) The square or an even number is
3) Without adding find the sum of 143454719111,
4) If a number hus i or 9 in the unit's place then its square ends in
5) The sum of two triangular numbers is a
number​

Answer 1

Step-by-step explanation:

1)

2) Odd and even square numbers

Squares of even numbers are even (and in fact divisible by 4), since (2n)2 = 4n2. Squares of odd numbers are odd, since (2n + 1)2 = 4(n2 + n) + 1. It follows that square roots of even square numbers are even, and square roots of odd square numbers are odd.

3)

4) If a number has 1 and 9 in unit place then it's square ends with digit 1.

5) Jence z is the sum of two triangular numbers iff 8z+2 is the sum of two squares, i.e. iff for every prime p of the form 4k+3 that divides 8z+2, νp(8z+2) is even. and z is the sum of two triangular numbers: 87180=(512)+(4152).

PLZ MARK ME AS BRAINLIEST I HAVE ATTENDED THE QUESTIONS EXCEPT 1 & 3 BCZ I DON'T KNOW SORRY FOR THAT

Answer 2

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