which of the following is the cube of an even natural number? (a) 3375 (b) 4913 (c) 1728 (d) 2197
Answers
Answer:
The correct answer to the given question is Option(c) 1728.
Step-by-step explanation:
1728 is the cube root of an even natural number.
- In the subject of mathematics, the cube root of a number that is supposed as y is the number x such that,
- All real numbers have exactly one real cube root.
- Natural numbers consist of all the positive numbers from zero to infinity. They are used for counting.
- Even natural numbers are those numbers that are even, which means they are exactly divisible by 2.
- Option a.3375:
= 15
15x15x15=3375
3375 is the cube root of 15.
15 is an odd number that is not divisible by 2. Therefore 3375 is not the cube root of an even natural number.
- Option b. 4913:
= 17
17x17x17=4913
4913 is the cube root of 17.
17 is an odd number that is not divisible by 2. Therefore 4913 is not the cube root of an even natural number.
- Option c.1728:
= 12
12x12x12=1728
1728 is the cube root of 12.
12 is an odd number that is divisible by 2. Therefore 1728 is the cube root of an even natural number.
- Option d.2197:
= 13
13x13x13=2197
2197 is the cube root of 13.
13 is an odd number that is not divisible by 2. Therefore 2197 is not the root of an even natural number.
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Answer:
Option (c) is the correct answer.
Step-by-step explanation:
As we know,
The product of 3 even natural numbers is always be even, i.e.,
The cube of an even number is always be even.
(a) 3375
Notice that the number 3375 is an odd number.
And the cube of an even number cannot be odd.
Thus, option (a) is incorrect.
(b) 4913
Notice that the number 4913 is an odd number.
And the cube of an even number cannot be odd.
Thus, option (b) is incorrect.
(c) 1728
Clearly, the number 1728 is an even number.
And the cube of an even number is always be even.
1728 =
This implies cube of 12 is 1728.
Thus, option (c) is correct.
(d) 2197
Notice that the number 2197 is an odd number.
And the cube of an even number cannot be odd.
Thus, option (d) is incorrect.
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