Simplifying Radicals. SWBAT –Simplify Square Root Radicals Warm – Up Identify the perfect square in each set. 1. 45 81 27 111 2. 156 99 8 25 3. 256 84.

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Presentation transcript:

Simplifying Radicals

SWBAT –Simplify Square Root Radicals Warm – Up Identify the perfect square in each set

SWBAT –Simplify Square Root Radicals Perfect Squares Perfect squares are the result of any integer times itself. Arithmetic perfect squares: 1, 4, 9, _____, _____, _____, _____, _____, _____... Algebraic perfect squares: x times itself, x 2 times itself, x 3 times itself, etc.. x 2, x 4, _____, _____, _____, _____, _____, _____... In general, x to any ________ power is a perfect square. To determine what each is a perfect square of, you should __________________ Example: x 36 is a perfect square of ___________ x6x6 x8x8 x 10 x 12 x 14 x 16 even divide the exponent by 2 x 18

Simplifying Square Roots Definition: A square root is said to be simplified if there are no perfect square factors of the radicand.

SWBAT –Simplify Square Root Radicals PRACTICE/HOMEWORK

Simplifying Higher Index Radicals Perfect Cubes and beyond Perfect cubes are the result of any integer times itself three times. Arithmetic perfect cubes: 1, 8, _____, _____, _____,... Algebraic perfect squares: x times itself three times, x 2 times itself three times, etc.. x 3, _____, _____, _____, _____,... In general, x to any ________ power is a perfect cube. To determine what each is a perfect cube of, you should __________________ Example: x 30 is a perfect cube of ___________ Multiple of 3 Divide the exponent by 3

SWBAT –Simplify Higher Power Radicals

*Please note that for cube roots (or any odd root), the absolute value is unnecessary. This is because it is possible to take an odd root of a negative number. These methods can be extended for any n th root.

SWBAT –Simplify Higher Order Radicals

SUMMARY A radical expression is in simplest form when the following three conditions have been met: 1.No radicands have perfect square factors other than 1. 2.No radicands contain fractions. 3.No radicals appear in the denominator of a fraction.

SWBAT –Simplify Radicals