CH 5 RADICALS LESSON 1 BASICS WITH RADICALS

CH 5 RADICALS LESSON 1 BASICS WITH RADICALS MIXED RADICALS ADDING/SUBTRACTING MIXED RADICALS

REVIEW: EVALUATE EACH OF THE FOLLOWING WITHOUT A CALCULATOR Answers:

FRACTIONAL EXPONENTS AND NTH ROOTS: The square root of a number is equivalent to having an exponent of ½

Ex: Without using a calculator, match each power with the value that it is equivalent to:

SIMPLIFYING RADICALS AND FRACTIONAL EXPONENTS To simplify or get rid of a square root, you will need to multiply two equivalent roots Review: Exponent Rules When multiplying two powers with the same base, add the exponents To simplify or get rid of a cube root, you will need to multiply three equivalent cube roots 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 each radical to a mixed radical

CONVERTING TO A MIXED RADICAL To simplify a radical with a square root, use perfect squares � To simplify a radical with a cube root, use perfect cubes � 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196…. . 8, 27, 64, 125, 216, 343 …. . Another method is to reduce the number to it’s prime factorization and then simplify to a mixed radical

Ex: Match each radical with it’s corresponding Mixed radical

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

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

Ex: Evaluate each of the following