5-5 Roots of Real Numbers

Objective: Students will be able to simplify

radicals.

What is a square root?• A square root is one of two equal factors of a

number.– For example, the square roots of 49 are both 7 and -7.

– In the above example, 7 is what is known as the principal square root (the nonnegative root when there is more than one real root).

• We can also find other roots of numbers, such as cubed roots, fourth roots, fifth roots, or nth roots.

Terminology

• Index: tells us what root we are looking for• Radicand: term underneath the radical sign

• Let’s start by simplifying some quick examples.

• When finding roots of variables, simply divide the exponent on the variable by the index.

• Examples:

• Now let’s work through some examples.

Simplify.1) 2) 3)

4) 5) 6)

Try these.7) 8) 9)

10) 11) 12)