Section 5.1 Basics with Radicals

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Presentation transcript:

Section 5.1 Basics with Radicals

I) Review: Squares and Cubes © Copyright all rights reserved to Homework depot: www.BCMath.ca

II) What are Radicals A radical is a symbol that involves the square root or nth root of a number A radical can also be viewed as a fractional exponent Entire Radicals vs Mixed Radicals

III) Properties of Radicals The nth root of a radical indicates the number of terms required to simplify a radical Suppose the nth root was “5”, you will need five factors to cancel out the root If you have more factors than the roots, then take out the factors that can be simplified and then leave the remaining factors inside the radical

Ex: Simplify each entire radical to a mixed radical A cube root means that you need a perfect cube to take it out of the root If you have too many factors, combine three together and leave the rest

Practice: Simplify and convert to a mixed radical:

IV) Converting Mixed Radicals to Entire Radicals When converting from mixed radicals back to entire radicals, each factor outside will go back into the radicals to the nth power

Ex: Arrange the following from least to greatest: Convert each mixed radical to complete radicals © Copyright all rights reserved to Homework depot: www.BCMath.ca

IV) Adding & Subtracting Radicals You can only add two polynomials if they are like terms Likewise, you can only add or subtract two radicals if they are “like radicals” Simplify a radical if the number inside the radical sign becomes the same © Copyright all rights reserved to Homework depot: www.BCMath.ca

Simplify the following: © Copyright all rights reserved to Homework depot: www.BCMath.ca

HW: assignment 5.1