Simplify Square Roots

**Simplify Square Roots**

To simplify square roots, we can make use of the **product rule for square roots**, which states that the product of two square roots is equal to the square root of the product for all real numbers.

**To Simplify the Square Root of a Constant:**

1) Write the constant as a product of the largest perfect square factor and another factor.

2) Use the product rule to write the expression as a product of square roots, with each square root containing one of the factors.

3) Find the square root of the perfect square factor.

Examples:

**To Simplify Square Roots Containing Variables:**

1) If the expression consists of a variable raised to an even power, the square root of the expression equals the variable raised to one-half of that power.

Examples:

2) If the variable contains an odd power, express it as the product of two factors, one having an exponent 1 and the other with an even exponent.

3) Use the product rule to simplify.

**Examples:**

**Practice**

**Answer Key**