Rewrite √45 in as a product of an integer and irrational square root.
show work
First, we need to find the prime factorization of 45.
45 = 3 × 3 × 5
Next, we can simplify the square root by taking out pairs of prime factors.
√45 = √(3 × 3 × 5)
We can take out one factor of 3 from the square root, leaving us with an integer outside the square root.
√45 = 3√(5)
Therefore, √45 can be written as the product of the integer 3 and the irrational square root √5.