No. Here is a proof by counterexample that it does not.
Given ab + bc + ca = 3:
Assume toward a contradiction that abc is a cube. Then a = b = c.
Without loss of generality, let a = 2, b = 2, and c = 2.
Then ab = 4, bc = 4, and ca = 4.
ab + bc + ca = 4 + 4 + 4 = 12.
Therefore, 12 = 3, which is false, and so the original statement is false.
Finding the square root of a positive integer involves identifying a number that, when multiplied by itself, equals the original integer, resulting in one non-negative solution. In contrast, finding the cube root of a positive integer determines a number that, when multiplied by itself twice (i.e., raised to the power of three), equals the original integer, yielding one real solution. The key difference lies in the operations involved: square roots deal with pairs of factors, while cube roots involve triplets. Additionally, cube roots can yield real solutions for negative integers, unlike square roots.
No, 121 is not a cube number. A cube number is the result of an integer multiplied by itself three times (n × n × n). The cube of integers around the square root of 121 (10) are 8 (2^3) and 27 (3^3), neither of which equals 121. Thus, 121 is classified as a square number (11 × 11), not a cube number.
No, 11025 is not a perfect cube. A perfect cube is an integer that can be expressed as the cube of another integer. The cube root of 11025 is approximately 22.2, which is not an integer, indicating that 11025 cannot be written as ( n^3 ) for any integer ( n ).
an integer
343 is a perfect cube because it can be expressed as (7^3) (7 multiplied by itself three times: (7 \times 7 \times 7 = 343)). In mathematics, a perfect cube is a number that can be formed by raising an integer to the third power. Since 7 is an integer and its cube equals 343, this confirms that 343 is indeed a perfect cube.
Finding the square root of a positive integer involves identifying a number that, when multiplied by itself, equals the original integer, resulting in one non-negative solution. In contrast, finding the cube root of a positive integer determines a number that, when multiplied by itself twice (i.e., raised to the power of three), equals the original integer, yielding one real solution. The key difference lies in the operations involved: square roots deal with pairs of factors, while cube roots involve triplets. Additionally, cube roots can yield real solutions for negative integers, unlike square roots.
No, 11025 is not a perfect cube. A perfect cube is an integer that can be expressed as the cube of another integer. The cube root of 11025 is approximately 22.2, which is not an integer, indicating that 11025 cannot be written as ( n^3 ) for any integer ( n ).
an integer
The integer is 26
If by cube you mean perfect cube (a cube of an integer), then no, and the nearest perfect cube is 81.
The number 784 is not a perfect cube. A perfect cube is defined as a number that can be expressed as the cube of an integer (i.e., (n^3) for some integer (n)). The cube root of 784 is approximately 9.24, which is not an integer, indicating that 784 cannot be represented as a whole number cubed.
2
Because they are square/cube of an integer.
A cube is any number multiplied by itself three times, eg 2 cubed = 2³ = 2×2×2 = 8; 1.5³ = 1.5×1.5×1.5 = 3.375 A perfect cube is an integer (whole number) that is the cube of an integer, eg 8 is a perfect cube as it is 2 cubed, but 9 is not a perfect cube as 9 = 2.08008382...³
45
x = 484
The smallest possible value of ( k ) if ( k ) is a perfect cube is ( 1 ), since ( 1^3 = 1 ). Perfect cubes are formed by multiplying integers by themselves three times, and the smallest integer, which is ( 1 ), yields the smallest perfect cube. Therefore, ( k = 1 ) is the answer.