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)