Jose says that100 is a perfect square. How can Jose justify his statement?
100 = 10x10 = 10^2
http://www.mathsisfun.com/definitions/perfect-square.html
What is the square root of 100?
4 ➕ 9
To justify whether 100 is a perfect square, Jose needs to understand the concept of perfect squares. A perfect square is a number that can be expressed as the product of two equal integers. For example, 9 is a perfect square because it can be expressed as 3 multiplied by 3 (3 x 3 = 9).
To determine if 100 is a perfect square, Jose can employ a couple of strategies:
1. Prime factorization: Jose can find the prime factors of 100, which are 2 and 5. If he finds pairs of the same prime factors, then 100 is a perfect square. In this case: 2 x 2 x 5 x 5 = 100. Since there are pairs of 2s and pairs of 5s, 100 is indeed a perfect square.
2. Using the square root: Jose can calculate the square root of 100, which is 10 (because 10 x 10 = 100). If the square root is a whole number, then the original number is a perfect square.
So, Jose can justify his statement that 100 is a perfect square by either showing the prime factorization or calculating the square root and confirming that it is a whole number.