Identifying the Perfect Cube Monomial- A Closer Look at 1×10, 8×8, 9×9, and 27×15

Which monomial is a perfect cube? This question often arises in mathematics, particularly when dealing with polynomials and algebraic expressions. In this article, we will explore the given monomials 1×10, 8×8, 9×9, and 27×15 to determine which one is a perfect cube.

A perfect cube is a number that can be expressed as the cube of an integer. In other words, it is the result of multiplying a number by itself three times. For example, 27 is a perfect cube because it can be written as 3 x 3 x 3. Now, let’s analyze each of the given monomials to determine if they are perfect cubes.

The first monomial is 1×10. To determine if it is a perfect cube, we need to check if there exists an integer that, when multiplied by itself three times, equals 1×10. In this case, there is no such integer, as 1×10 is not a perfect cube.

The second monomial is 8×8. To determine if it is a perfect cube, we need to check if there exists an integer that, when multiplied by itself three times, equals 8×8. In this case, the integer is 2, as 2 x 2 x 2 equals 8×8. Therefore, 8×8 is a perfect cube.

The third monomial is 9×9. Similar to the previous case, we need to check if there exists an integer that, when multiplied by itself three times, equals 9×9. The integer in this case is 3, as 3 x 3 x 3 equals 9×9. Thus, 9×9 is also a perfect cube.

Finally, we have the monomial 27×15. To determine if it is a perfect cube, we need to check if there exists an integer that, when multiplied by itself three times, equals 27×15. However, this monomial is not a perfect cube, as no integer can be multiplied by itself three times to result in 27×15.

In conclusion, among the given monomials, 8×8 and 9×9 are perfect cubes, while 1×10 and 27×15 are not. Understanding the concept of perfect cubes is crucial in various mathematical fields, such as algebra, geometry, and calculus.