# Math 10 Lesson 1 5 Mixed And Entire Radicals

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Example 3Simplify 4 162 .In general, the larger the index the harder it is to spot appropriate factors to try. Adifferent strategy from the one used in Examples 1 and 2 is to factor the radicand intoits prime factors. Since we are dealing with the 4th root, we are looking for prime factorsthat repeat 4 times. The prime factorization of 162 is 2·3·3·3·3 or 2·34 2·81. Thus,4162 4 2 81 4 2 4 81 34 2Example 4Simplify 162 98Note that we cannot add 162 and 98 together: 162 98 162 98There is no obvious way to simplify this expression. Thus, we try to simply each radicaland then see what we can do from there.162 98 81 2 49 2 9 2 7 2 16 2Note, the Pearson text book uses prime factorization as its prime strategy. While it is a goodstrategy to use at times, it is not wise to use it as your only strategy when solving problems. Itis wise to approach problem solving with a more playful and open attitude that is capable ofseeing new and creative ways to solve problems. A playful, creative approach also has thebenefit of removing some of the boredom and tedium of some math assignments.Question 1Simplify the following:754Dr. Ron LichtL1–5 Mixed and entire learning.com

V. Nasty question of the dayExample 83 1.732 and without using a calculator determine a decimalapproximation for 12 .Given thatPerhaps we could change12 4 3Since12 into a mixed radical and then see where that leads us. 2 31.7323 2 3 2 1.732 3.464Therefore 12 3.46412Given that 2 1.4142 and without using a calculator determine a decimal approximationfor each radical.(a)200(b)20000(c)8(d)18(e)32(f)50Dr. Ron LichtL1–5 Mixed and entire radicals5www.structuredindependentlearning.com

11. Here is a student’s solution for writing as an entire radical.83 2 8 3 2 3 2 3 2 3 2 2 34Identify an error the student made, then write the correct solution.12. A student simplified a radical as shown:96 4 48 2 48 2 8 6 2 4 6 8 6Identify the errors the student made, then write a correct solution.13. Simplify the radicals in each list. What patterns do you see in the results? Write the next 2radicals in each list.a)4c)8400800400008000014. The largest square in this diagram has side length 8 cm. Calculatethe side length and area of each of the two smaller squares.Write the radicals in simplest form.Dr. Ron LichtL1–5 Mixed and entire radicals7www.structuredindependentlearning.com

Dr. Ron Licht 1 www.structuredindependentlearning.com L1–5 Mixed and entire radicals Math 10 Lesson 1-5 Mixed and Entire Radicals I. Entire and mixed radicals An entire radical is a number in a radical with no coefficient or multiplying number in front of the radical. 23 3 2000 4 162 are all examples of entire radicals. A mixed radical is a number in a radical with a coefficient or .

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