Algebra Review Radical Expressions page 280 Essential Question Can you solve an equation with a square root radical?

Simplifying Radicals In the next chapters, work will be done with radicals, specifically square root radicals, such as _____ or _____.

If n is a positive integer that is greater than 1 and What is a RADICAL? If n is a positive integer that is greater than 1 and a is a real number then, where n is called the index, a is called the radicand, and the symbol √ is called the radical.

Square Root - definition from Wikipedia In mathematics, a square root (√) of a number x is a number r such that r2 = x, or in words, a number r whose square (the result of multiplying the number by itself) is x. Every non-negative real number x has a unique non-negative square root, called the principal square root and denoted with a radical symbol as √x. For example, the principal square root of 9 is 3, denoted √9 = 3, because 32 = 3 × 3 = 9. If otherwise unqualified, "the square root" of a number refers to the principal square root: the square root of 2 is approximately 1.4142. Square roots often arise when solving quadratic equations, or equations of the form ax2 + bx + c = 0, due to the variable x being squared. Every positive number x has two square roots. One of them is √x, which is positive, and the other −√x, which is negative. Together, these two roots are denoted ±√x. Square roots of integers that are not perfect squares are always irrational numbers: numbers not expressible as a ratio of two integers. For example, √2 cannot be written exactly as m/n, where n and m are integers.

Square Root - easy definition A number that when multiplied by itself equals a given number. Root A number that, when multiplied by itself some number of times, equals a given number.

Perfect Squares Know these! 12 = 1 22 = 4 32 = 9 42 = 16 52 = 25 62 = 36 72 = 49 82 = 64 92 = 81 102 = 100 112 = 121 122 = 144 132 = 169 142 = 196 152 = 225 Perfect Squares Know these!

A RADICAL is in simplest form when … #1 No perfect square factor, other than one, is ________ the radical sign. under

Use this property from algebra!

Example (a)

Example (b)

Example (1)

Example (2)

Example (3)

Example (4)

Example (5)

Example (6)

Example (7)

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Example (9)

Example (13)

Example (14)

A RADICAL is in simplest form when … #2 No fraction, is ________ the radical sign. under

Use this property from algebra!

Example (a)

Example (b)

A RADICAL is in simplest form when … #3 No fraction,has a radical in the _________________. denominator

Rationalizing the Denominator, Use a method called … Rationalizing the Denominator, by using this pattern.

Example (a) Multiplying by 1 does not change it’s value.

Example (b) Multiplying by 1 does not change it’s value.

Example (a) - AGAIN!

Example (b) - AGAIN!

Example (10)

Example (11)

Example (12)

RADICALS must always be expressed in simplest form! Why? So you are able to recognize the patterns.

Can you solve an equation with a square root radical? Assignment Algebra Review on page 280 1 to 29 odd numbers Assignment Written Exercises on page 288 1 to 15 odd numbers Be prepared for a quiz on Simplifying Radicals! Can you solve an equation with a square root radical?