Question

what is the only number greater than 1 and less than 100 that is both a sqayre number and a cube number

Answer 1

The only number between 1 and 100 that is both a square and a cube is 64, which is 2 raised to the 6th power, as six is the least common multiple of two and three.

Step-by-step explanation:

Finding a Number that is Both a Square and a Cube

To find a number greater than 1 and less than 100 that is both a square number and a cube number, we need to look for a power that is both the second power (a square) and the third power (a cube). This would be the sixth power of a number because six is the least common multiple of two and three. The smallest number with this property is 26 which is 64. Therefore, the only number that is both square and cube between 1 and 100 is 64.

Raising a number to a power, such as integer powers, is a fundamental concept in algebra. For product of powers like xpxq, the rule is xp+q. When cubing of exponentials, you cube the digit term and multiply the exponent by 3. When we express numbers in scientific notation, we often use integer powers such as 106 to simplify large numbers.

Answer 2

The only number between 1 and 100 that is both a square number and a cube number is 64.

Step-by-step explanation:

The only number between 1 and 100 that is both a square number and a cube number is 64.

A square number is a number that can be obtained by multiplying a number by itself. For example, 2² = 4 and 3² = 9.

A cube number is a number that can be obtained by multiplying a number by itself twice. For example, 2³ = 8 and 3³ = 27.

To find this number, you can start by checking the perfect squares less than or equal to 100. The perfect squares less than 100 are 1, 4, 9, 16, 25, 36, 49, and 64.

Next, check which of these numbers are also perfect cubes. The perfect cubes of 1, 4, 9, 16, 25, 36, 49, and 64 are 1, 64, and 729. The only number that is both a square number and a cube number between 1 and 100 is 64.