Introduction to Radicals

This symbol is the radical or the radical sign Radical Expressions Finding a root of a number is the inverse operation of raising a number to a power. radical sign index radicand This symbol is the radical or the radical sign The expression under the radical sign is the radicand. The index defines the root to be taken.

Square Roots A square root of any positive number has two roots – one is positive and the other is negative. If a is a positive number, then is the positive (principal) square root of a and is the negative square root of a. Examples: non-real #

What does the following symbol represent? The symbol represents the positive or principal root of a number. What is the radicand of the expression ? 5xy

What does the following symbol represent? The symbol represents the negative root of a number. What is the index of the expression ? 3

What numbers are perfect squares? 1 • 1 = 1 2 • 2 = 4 3 • 3 = 9 4 • 4 = 16 5 • 5 = 25 6 • 6 = 36 49, 64, 81, 100, 121, 144, ...

Perfect Squares 64 225 1 81 256 4 100 289 9 121 16 324 144 25 400 169 36 196 49 625

Simplify = 2 = 4 = 5 This is a piece of cake! = 10 = 12

Simplifying Radicals

Simplify = = = = = = = = = = Perfect Square Factor * Other Factor LEAVE IN RADICAL FORM = = = = = =

Simplify = = = = = = = = = = Perfect Square Factor * Other Factor LEAVE IN RADICAL FORM = = = = = =

Simplify .

Simplify 3x6 3x18 9x6 9x18

+ To combine radicals: combine the coefficients of like radicals Combining Radicals + To combine radicals: combine the coefficients of like radicals

Simplify each expression

Simplify each expression: Simplify each radical first and then combine.

Simplify each expression: Simplify each radical first and then combine.

Simplify = = = = = = = = = = Perfect Square Factor * Other Factor LEAVE IN RADICAL FORM = = = = = =

Simplify each expression

Simplify each expression

Multiplying Radicals * To multiply radicals: multiply the coefficients and then multiply the radicands and then simplify the remaining radicals.

Multiply and then simplify

Dividing Radicals To divide radicals: divide the coefficients, divide the radicands if possible, and rationalize the denominator so that no radical remains in the denominator

That was easy!

42 cannot be simplified, so we are finished. This cannot be divided which leaves the radical in the denominator. We do not leave radicals in the denominator. So we need to rationalize by multiplying the fraction by something so we can eliminate the radical in the denominator. 42 cannot be simplified, so we are finished.

This can be divided which leaves the radical in the denominator This can be divided which leaves the radical in the denominator. We do not leave radicals in the denominator. So we need to rationalize by multiplying the fraction by something so we can eliminate the radical in the denominator.

This cannot be divided which leaves the radical in the denominator This cannot be divided which leaves the radical in the denominator. We do not leave radicals in the denominator. So we need to rationalize by multiplying the fraction by something so we can eliminate the radical in the denominator. Reduce the fraction.

Simplify = X = Y3 = P2X3Y = 2X2Y = 5C4D5

Simplify = = = =

worksheet --- Non-Perfect Squares Classwork: Packet in Yellow Folder under the desk --- 2nd page Homework: worksheet --- Non-Perfect Squares (#1-12)