Radicals (Simplify, Add/Subtract, Multiply)

Alyxandria Hodgin
Mind Map by Alyxandria Hodgin, updated more than 1 year ago
Alyxandria Hodgin
Created by Alyxandria Hodgin over 4 years ago
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Description

9th grade Math Mind Map on Radicals (Simplify, Add/Subtract, Multiply), created by Alyxandria Hodgin on 02/15/2017.

Resource summary

Radicals (Simplify, Add/Subtract, Multiply)
  1. Simplifying
    1. Factor the Radical
      1. Find the factors of the number inside the box (one of them should be a perfect square
        1. √50 factors to √2*√25 because 2*25=50
      2. Simplify the perfect square (i.e. √25=5)
        1. Take the simplified square, multiply it by the imperfect square
          1. Like this: 5√2
          2. The outside number may be positive or negative
            1. Finished simplification: ±5√2
            2. Algebra Example
              1. √20x^2y^4
                1. Factor 20
                  1. multiply x^2y^4 by 1/2
                    1. xy^2
                    2. Recombine with variables outside of the box
                      1. ±2xy^2√5
                2. Adding/Subtracting
                  1. Same-Root
                    1. Add/Subtract the numbers in front
                      1. 2√3+5√3=7√3
                    2. Different Root
                      1. Factor until you have the same root
                        1. √54+√24
                          1. √54 factors to √9*√6, which equals 3√6
                            1. √24 factors to √4*√6, which equals 2√6
                              1. 2√6+3√6=5√6
                        2. Multiplying
                          1. Multiply numbers inside the roots
                            1. √10*√50=√150 because 10*15=150
                            2. Factor the result
                              1. √150 factored is √25 and √6
                                1. Simplify
                                  1. √25=5, so the final answer is 5√6
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