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To be a perfect square, all the primes in a number's prime factorisation must have an even power

To be a perfect cube, all the primes in a number's prime factorisation must a power that is a multiple of 3

→ To be a perfect square, all the primes in a number's prime factorisation must a power that is a multiple of 3 and a multiple of 2, ie the power must be a multiple of 6

The smallest prime is 2

2⁶ = 64 = (2³)² = 8² = (2²)³ = 4³

2¹² = 4096 (too large)

3⁶ = 729 (too large)

There is also 1 = 1² = 1³

Thus the whole numbers less than 100 which are both perfect squares and perfect cubes are 1 and 64.

Q: What whole number is less than 100 that is both a perfect square and a perfect cube?

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It is both because 1,000,000 is a perfect cube and a perfect square number

A perfect square is the square of an integer, i.e., an integer multiplied by itself. For example, 25 is a perfect square, because 5 x 5 = 25. But, in literal mathematical terms, a perfect number is a positive integer that is the sum of its proper positive divisors, excluding the number itself. A square number is also called a "perfect square", so an example of a square number is above. So, a perfect square number would have to be a number that is both perfect and square, and there are yet to be any of these numbers "discovered".

0, 1To be both a square and a cube, the number has to be a sixth power. You don't need to calculate though, since 06=0 and 16=1.The next 2 sixth powers are 26=64 and 36=729.

To find a number that is both a perfect square and a perfect cube, we must solve x2 = x3 over x ∈Z+. The only two solutions to this equation are 0 and 1, or x = {0,1}. Therefore, zero and one are the only two numbers that are both perfect squares and perfect cubes. --In easier terms: a perfect square is a number that can be "square rooted" and have no remainder. Like, 144. The square root is 12 therefore 144 is a perfect square. A perfect Cube is the same except that it must be "cubed rooted". Like 27. The cube root of this number is 3 therefore 27 is a perfect cube.

6443 = 6482 = 64

Related questions

it is not possible. Here is a simple explanation. Let m & n be whole numbers, so m² & n² are both perfect square numbers. Now multiply them together, and: m² * n² = (m*n)². Since m and n are both whole numbers, then m*n is a whole number, so (m*n)² is a perfect square.

It is both because 1,000,000 is a perfect cube and a perfect square number

There is not a number that is a perfect square and perfect cube between 1 and 25.There is not a number that is a perfect square and perfect cube between 1 and 25.There is not a number that is a perfect square and perfect cube between 1 and 25.There is not a number that is a perfect square and perfect cube between 1 and 25.

It is the smallest composite number that is both a perfect square and a perfect cube.

Basically a perfect square is a number like 81 or 100. When these numbers are square rooted, they equal whole numbers like 9 or 10. An imperfect square is a number that when is square rooted equals and repeating decimal, like 29 when square rooted equals 5.385164807134504... (Note: Both even and odd number can be imperfect or perfect squares.)

A perfect square is the square of an integer, i.e., an integer multiplied by itself. For example, 25 is a perfect square, because 5 x 5 = 25. But, in literal mathematical terms, a perfect number is a positive integer that is the sum of its proper positive divisors, excluding the number itself. A square number is also called a "perfect square", so an example of a square number is above. So, a perfect square number would have to be a number that is both perfect and square, and there are yet to be any of these numbers "discovered".

1 (1x1x1 or 1x1)

The root of a perfect square will be an integer, but will be both the positive and negative values. For instance, the square root of 4 is plus or minus 2 (±2), as both integral answers are valid. The positive real root is the answer that many books give. It is sometimes called the primary root. But the key point is both roots are valid.

In general, not usually.The square root of an irrational number is always irrational.The square root of a rational number is usually irrational, but not always. You can tell by this test:If both the numerator and denominator of the number expressed as a simplified fraction are perfect square numbers (a number whose square root is a whole number), then the square root of the whole fraction will be rational.Example: Sqrt(4) =2 (the positive one). Sqrt(1) = 1. Both are perfect squares.So sqrt(1/4) = sqrt(1)/sqrt(4) = 1/2. Another one: sqrt(4/9) = 2/3.

0, 1To be both a square and a cube, the number has to be a sixth power. You don't need to calculate though, since 06=0 and 16=1.The next 2 sixth powers are 26=64 and 36=729.

To find a number that is both a perfect square and a perfect cube, we must solve x2 = x3 over x ∈Z+. The only two solutions to this equation are 0 and 1, or x = {0,1}. Therefore, zero and one are the only two numbers that are both perfect squares and perfect cubes. --In easier terms: a perfect square is a number that can be "square rooted" and have no remainder. Like, 144. The square root is 12 therefore 144 is a perfect square. A perfect Cube is the same except that it must be "cubed rooted". Like 27. The cube root of this number is 3 therefore 27 is a perfect cube.

25 is both square and composite