Question

simplifying square roots

1. write the prime factorization of the

______.

• ______ factorization is the number

or expression written as a product of
its prime factors.

• recall that prime numbers are whole

numbers ______ than one that
have exactly two factors, ____ and the
number itself.

1. apply the ______ property of square

roots. write the radicand as a product,
forming as many perfect square roots as
possible.

1. simplify.

Explanation:

1. For the first blank in step 1, when simplifying square roots, we start with the prime factorization of the radicand (the number inside the square root). The next blank: Prime factorization is the product of prime factors. For prime numbers: they are whole numbers greater than one, with factors 1 and themselves.
2. In step 2, the property used is the product property of square roots (\(\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\) for \(a\geq0,b\geq0\)), which allows us to split the radicand into a product of perfect squares and other factors.

Answer:

1. radicand; Prime; greater; 1
2. product
3. (This step is to simplify using the previous steps, e.g., take square roots of perfect squares)