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What is perfect square and perfect cube?
The square root of a perfect square and the cube root of a perfect cube is always an integer. A perfect square is a number multiplied by itself. A perfect cube is a number multiplied by itself twice. Example: 3 x 3 is 9, the square of 3 3 x 3 x 3 is 27, the cube of 3
What is a perfect cube number?
A perfect cube is the cube of an integer (whole number). This means that, for n to be a perfect cube, n = x3, x∈ℤ Eg. ±1 [=(±1)3], 8 [=(±2)3], ±27 [= (±3)3], etc.
Is 30 a perfect cube?
No, 30 is not a perfect cube. A perfect cube is a number that can be expressed as the cube of an integer, such as (1^3 = 1), (2^3 = 8), or (3^3 = 27). The cube root of 30 is approximately 3.11, which is not an integer, confirming that 30 cannot be written as the cube of any whole number.
What is the largest three digit perfect cube?
The largest three-digit perfect cube is 729, which is (9^3). The next perfect cube, (10^3), equals 1000, which exceeds three digits. Therefore, 729 is the highest three-digit number that can be expressed as a perfect cube.
What are the perfect cubes between 10 and 30?
The perfect cubes between 10 and 30 are 27, which is the cube of 3 (3^3). The next perfect cube, 64 (4^3), exceeds 30, while the perfect cubes below 10 are 1 (1^3) and 8 (2^3). Therefore, 27 is the only perfect cube in that range.
What is the largest perfect cube factor of 189?
To find the largest perfect cube factor of 189, we first need to factor it into its prime components. The prime factorization of 189 is (3^3 \times 7^1). The largest perfect cube that can be formed from these factors is (3^3), which equals 27. Therefore, the largest perfect cube factor of 189 is 27.
Which is the only 3 digit no that is a perfect square and a perfect cube?
729
Is 11025 a perfect cube?
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 ).
Is nine a perfect cube?
no it is not 4 is a perfect cube
How is 784 a perfect cube?
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.
When x is a perfect square what is true about the cube of x?
When ( x ) is a perfect square, it can be expressed as ( x = n^2 ) for some integer ( n ). The cube of ( x ) is then ( x^3 = (n^2)^3 = n^6 ). Since ( n^6 ) is also a perfect square (as ( n^6 = (n^3)^2 )), it follows that the cube of any perfect square is itself a perfect square. Thus, when ( x ) is a perfect square, ( x^3 ) is also a perfect square.
Is 77 a cube number?
If by cube you mean perfect cube (a cube of an integer), then no, and the nearest perfect cube is 81.
