Question

please answer this question proof of workings​​

Answer 1

Answer:

1. False . Cube of even natural numbers is even.
2. False.sum of cubes of first n natural numbers is = (n(n+1)/2)2.
3. True Cube of negative integer is negative.
4. True. Because cube of 3 is 27 and unit digit is 7.

Answer 2

$\sf\purple{ QUESTION :- }$

1. Cube of even natural number is odd

$\sf\blue{ ANSWER :- }$

➜ False

Reason - Multiplication of 3 even numbers (the cube roots), will always be even

Example - 2³ = 2 × 2 × 2 = 8

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$\sf\purple{ QUESTION :- }$

2. the sum of cubes of first n natural numbers is equal to the cube of their sum.

$\sf\blue{ ANSWER :- }$

➜ False

Reason - the sum of cubes of first n natural numbers is equal to the Square of their sum

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$\sf\purple{ QUESTION :- }$

3. Cube of negative integer is negative

$\sf\blue{ ANSWER :- }$

➜ True

Reason - Cubes always involve multiplying a number by itself three times, so if the number is negative the cube will always be negative .

Example - -9³ = -9 × -9 × -9 = -729

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$\sf\purple{ QUESTION :- }$

4. Cube of numbers ending in 3 end in 7

$\sf\blue{ ANSWER :- }$

➜ True

Reason - the cubes of the numbers ending in digits 3 or 7 ends in digits 7 or 3, respectively.

Example - 23³ = 23 × 23 × 23 = 12167

Example - 27³ = 27 × 27 × 27 = 19683