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Adding and Subtracting Surds
Slideshow 8, Mr Richard Sasaki, Mathematics
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Objectives Be able to convert numbers in index form into fractions and surds Understand the values of surds that cannot be simplified Be able to add and subtract surds together
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Index Form Let’s review some rules about index form. 4 1 2 = 4 = ±2
= 4 = ±2 = 1 36 6 −2 = 7 7 7 − 1 2 = = = Writing numbers in surd form can help us simplify them further.
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Index Form Examples Write 12 1 2 in surd form. 12 1 2 = 12 = 4 ∙ 3 =
= 12 = 4 ∙ 3 = 2 3 Write 24 − in surd form. 24 − 1 2 = = = = = 6 12 Just try to remember that 𝑥 = 𝑥 and 𝑥 − 1 2 = 1 𝑥 . If 1 𝑥 is a surd then the denominator must be changed to an integer.
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Simplifying Surds Surds are often in the form… 𝑎 𝑏 Radicand
𝑎 𝑏 Radicand If 𝑎 𝑏 is in its simplest form, what values can 𝑏 take? 2, 3, 5, 6, 7, 10, … These are the numbers that do not have square factors (other than 1).
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5 3 2 4 3 21, 22, 23, 26, 29, 30 2 24 45 10 10 1 2 1 9 22 22 2 4 2 8 5 35 5 55 2 4 5 2 3
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Adding and Subtracting Surds
How can we simplify ? 3 3 If the radicands are the same, we can easily add roots together. Example If there are fractions, we need to make the denominators the same too. Simplify =
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Adding and Subtracting Surds
Can we simplify ? No we can’t. Both 3 and 5 are in their simplest forms. So we just leave it the same. = Example Simplify =3∙ ∙2 5 =
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=3+4=7 but = 25 =5. ∴ 𝑎 + 𝑏 ≠ 𝑎+𝑏 6 3 4 5 −6 11 3 −7 3 3+2 5 30 2 14 6 4 − 17 9 3 8
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3 3 −2 5 26 3 −10 13 20 and 2 25 and 2.5 The radicand multiplied by 100 gives the same result multiplied by 10. (i.e if 𝑥 =𝑦, 100𝑥 =10𝑦). 571 =23.9, =239 to 3 s.f each. 3 6 5 5
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Answers – Part 3 6 6 588 25
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