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§ 7.4

§ 7.4. Adding, Subtracting, and Dividing Radical Expressions. Combining Radicals. EXAMPLE. Simplify (add or subtract) by combining like radical terms:. SOLUTION. Apply the distributive property. Simplify. Group like terms. Apply the distributive property. Simplify.

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§ 7.4

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  1. §7.4 Adding, Subtracting, and Dividing Radical Expressions

  2. Combining Radicals EXAMPLE Simplify (add or subtract) by combining like radical terms: SOLUTION Apply the distributive property. Simplify. Group like terms. Apply the distributive property. Simplify. Blitzer, Intermediate Algebra, 5e – Slide #2 Section 7.4

  3. Simplifying Radicals Blitzer, Intermediate Algebra, 5e – Slide #3 Section 7.4

  4. Simplifying Radicals EXAMPLE Simplify using the quotient rule: SOLUTION Blitzer, Intermediate Algebra, 5e – Slide #4 Section 7.4

  5. Combining Radicals Blitzer, Intermediate Algebra, 5e – Slide #5 Section 7.4

  6. DONE

  7. Combining Radicals EXAMPLE Divide and, if possible, simplify: SOLUTION In each part of this problem, the indices in the numerator and the denominator are the same. Perform each division by dividing the radicands and retaining the common index. Divide the radicands and retain the common index. Divide factors in the radicand. Subtract exponents on common bases. Blitzer, Intermediate Algebra, 5e – Slide #7 Section 7.4

  8. Combining Radicals CONTINUED Simplify. Factor using the greatest perfect square factor. Factor into two radicals. Simplify. Divide the radicands and retain the common index. Divide factors in the radicand. Subtract exponents on common bases. Blitzer, Intermediate Algebra, 5e – Slide #8 Section 7.4

  9. Combining Radicals CONTINUED Simplify. Factor using the greatest perfect square factor. Factor into two radicals. Simplify. Blitzer, Intermediate Algebra, 5e – Slide #9 Section 7.4

  10. Combining Radicals Important to remember: Like radicals have the same indices and radicands. Like radicals can be added or subtracted using the distributive property. In some cases, you cannot see that radicals are “like” until you simplify them. When attempting to combine radicals, you should simplify the radicals first. Then you may see that you have like radicals that can be combined. Are we like? You don’t look like me. Yep. I’m 2 square roots of 3 and you are 5 square roots of 3. We have the same indices and radicands. We’re like! Let’s see…2 of them + 5 of them = 7 of them Blitzer, Intermediate Algebra, 5e – Slide #10 Section 7.4

  11. Combining Radicals Apples to apples, oranges to oranges,… you can only add “like” things…. Two or more radical expressions that have the same indices and the same radicands are called like radicals. Like radicals can be combined under addition in exactly the same way that we combined like terms under addition. Examples of this process follow. 2 elephants + 3 elephants = 5 elephants but 5 tigers + 3 gorillas = ??? Blitzer, Intermediate Algebra, 5e – Slide #11 Section 7.4

  12. Combining Radicals EXAMPLE Simplify by combining like radical terms, if possible: SOLUTION Factor the radicands using the greatest perfect square factors. Take the square root of each factor. Apply the distributive property. Blitzer, Intermediate Algebra, 5e – Slide #12 Section 7.4

  13. Combining Radicals CONTINUED Simplify. Factor the radicands using the greatest perfect cube factors. Take the cube root of each factor. Apply the distributive property. Simplify. Blitzer, Intermediate Algebra, 5e – Slide #13 Section 7.4

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