Algebra 1 Chapter 11 1 Simplifying Radical Expressions

Algebra 1 ~ Chapter 11. 1 Simplifying Radical Expressions

Warm Up – Simplify each expression a. ) √ 9 = b. ) √ 100 = c. ) √ 36 = d. ) √ 49 = e. ) √ 1 =

List of the first 15 Perfect Squares You MUST know this list!! 1 36 121 4 49 144 9 64 169 16 81 196 25 100 225

Ø An expression that contains a radical sign (√ ) is a radical expression. Ø There are many types of radical expressions (such as square roots, cube roots, fourth roots, and so on), but in this chapter, you will study radical expressions that contain only square roots. Ø The expression under a radical sign is the radicand. * A radicand may contain numbers, variables, or both.

Simplest Radical Form – An expression containing square root is in simplest form when… Ø the radicand has no perfect square factors other than 1 Ø the radicand has no fractions Ø there are no square roots in any denominator.

Ex. 1: Simplify each expression a. ) √ 24 b. ) √ 45 = √ 4 · √ 6 = √ 9 · √ 5 = 2√ 6 = 3√ 5 Simplest radical form!

Example 1 C – Simplify the radical expression Factor the radicand using perfect squares.

Ex. 1 – Simplify the radical expression d. ) e. )

Ex. 2 – Simplify each radical expression a. ) √ 12 b. ) √ 90 c. ) 2√ 36 d. ) √ 75 e. ) √ 147 f. ) -1√ 52

Ex. 3 – Simplify the radical expression Perform the indicated operation on the radicals. Leave answer in simplest radical form.

Ex. 4 – Simplify each expression a. ) √ 3 · √ 15 b. ) √ 2 · √ 24 c. ) 2√ 3 · 3√ 3 d. ) 4√ 5 · 2√ 6

Simplifying Square Roots with Variables Remember, 4 x x 2 x 3 x 4 x 5 √x x 2√x x 3√x x 4√x

Ex. 5 A – Simplify Factor the radicand using perfect squares. Simplify and rewrite with #s first, then radicals.

Ex. 5 B – Simplify Factor the radicand using perfect squares. Simplify and rewrite with #s first, then radicals.

Ex. 6 – Simplify a. ) b. ) c. )