Number of perfect squares of 4500 = 2×2×2

Explanation:
1. Prime Factorization of 4500:
- To find the number of perfect squares of 4500, we first need to factorize 4500 into its prime factors.
- Prime factorization of 4500 = 2 × 2 × 3 × 3 × 5 × 5 = 2^2 × 3^2 × 5^2.
2. Finding Perfect Squares:
- In order to find the perfect squares, we pair up the prime factors in twos.
- Each pair represents a perfect square because when multiplied, they yield a square of the prime number.
- In this case, we have 2 pairs of 2's, 2 pairs of 3's, and 2 pairs of 5's.
3. Calculating the Number of Perfect Squares:
- Each pair of prime factors represents a perfect square.
- Therefore, the number of perfect squares of 4500 is equal to the product of the number of pairs of each prime factor.
- In this case, we have 2 pairs of 2's, 2 pairs of 3's, and 2 pairs of 5's.
- So, the number of perfect squares of 4500 = 2 × 2 × 2 = 8.
4. Conclusion:
- The number of perfect squares of 4500 is 8, which is represented by 2×2×2 in terms of prime factors.