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Solve for the combined length of given pipes, find exact lengths, and simplify surds by identifying square factors and collecting like terms. Learn the methods for simplifying surds and multiplying surd terms together.
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Surds Starter 2. What is the exact value for the combined length of the pipes, answer as one term. 1. Find the exact lengths of these pipes 3cm 2cm 5cm 3cm 2cm 7cm 1cm 6cm
Surds Starter 2. What is the exact value for the combined length of the pipes, answer as one term. 1. Find the exact lengths of these pipes 3cm 7cm 2cm 5cm 6cm 3cm 1cm 1cm 5cm 2cm 7cm 3cm 1cm 6cm 3cm 2cm
Surds Starter 2. What is the exact value for the combined length of the pipes, answer as one term. 1. Find the exact lengths of these pipes 3cm 7cm 2cm 5cm 6cm 3cm 2cm 1cm 5cm 2cm 7cm 3cm 1cm 3cm 6cm 2cm
Surds Bronze: Simplify a single surd by identifying square factors of the root number Silver: Simplify multiple surd terms by collecting like terms Gold: Multiply two to four surd terms together and then simplify
Bronze: Simplify a single surd by identifying square factors of the root number Method 1 – Prime Number Decomposition Example Note You can of course split the number into its factors in other ways and still get the same final answer. Decompose into prime factors. x Top Tip Never be afraid to write a list of primes before you start to help you focus 2, 3, 5, 7, 9, 11, 13, 17, 19, 23, 29, 31, …. x x x Rearrange to collect like terms. x x x x Simplify. Ans:
Bronze: Simplify a single surd by identifying square factors of the root number Method 2 – Square Number Decomposition Example Note Sometimes you will find more than one square factor, wither look for the biggest or decompose it and multiply all the smaller squares together. Find a square factor. x Top Tip Never be afraid to write a list of squares before you start to help you focus 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, …. Simplify. Ans: x
Bronze: Simplify a single surd by identifying square factors of the root number Question 2: Un-simplify e.g. Question 1: Simplify e.g f) f) a) a) g) b) g) b) h) c) h) c) i) d) i) d) j) e) j) e)
Bronze: Simplify a single surd by identifying square factors of the root number ANSWERS Question 2: Un-simplify e.g. Question 1: Simplify e.g f) a) a) f) g) b) g) b) h) c) h) c) i) d) i) d) j) e) j) e)
Silver: Simplify multiple surd terms by collecting like terms Note Collecting like surds is collecting like term in algebra because surds are just numbers. Examples of Collecting like Surds + - + + + + 1. = 4 = 3 2. =2 2 4. - + - = 2 2 + + + 3. =2() 2 - + + = 5 4 + - + 6. 5. = 8 = 2()
Silver: Simplify multiple surd terms by collecting like terms Question 4: Un-simplify – turn theses into 4 or 5 terms, e.g. 3 = + - + Question 3: Simplify e.g. + + + = 4 a) + + + a) b) - + + b) c) - - + c) d) - + + - d) e) - - + e)
Silver: Simplify multiple surd terms by collecting like terms Question 4: Un-simplify – turn theses into 4 or 5 terms, e.g. 3 = + - + Question 3: Simplify e.g. + + + = 4 a) a) b) There are lots of possible solutions to these questions so ask a partner to switch with you and assess each other’s solutions. b) c) c) d) - + 6or - ) or equivalent d) e) - - or -( + ) e)
Gold: Multiply two to four surd terms together and then simplify Question 6: By only multiplying terms, expand using surds in all your terms. e.g. Question 5: Multiply e.g. x = = x x f) x a) a) f) x g) g) x b) b) x 2 x x h) h) x x c) c) x x x x 8 d) i) d) i) x 2 e) e) x x x 2 x 5) j) j) Question 8: By only multiplying terms, expand and un-simplify creating 3 or 4 surd terms e.g. Question 7: Multiply and Simplify e.g. x x = 2 2 = x x x X a) a) x x b) b) x x x - c) c) - x x x - d) 136 d) x x x e) e)
Gold: Multiply two to four surd terms together and then simplify ANSWERS Question 6: By only multiplying terms, expand using surds in all your terms. e.g. Question 5: Multiply e.g. x = = x )3 x f) a) )2 f) a) )3 x g) b) )2 g) b) )2 x h) x c) h) c) x )4 x d) i) d) i) )3 e) )2 x j) e) j) Ask a partner to check any alternative solutions to these problems Question 7: Multiply and Simplify e.g. Question 8: By only multiplying terms, expand and un-simplify creating 3 or 4 surd terms e.g. x x = 2 a) 2 = x x 280 b) a) There are lots of possible solutions to these questions so ask a partner to switch with you and assess each other’s solutions. c) b) d) c) e) d) e)
Gold: Multiply two to four surd terms together and then simplify Question 6: By only multiplying terms, expand using surds in all your terms. e.g. Question 5: Multiply e.g. = x x = x f) x a) a) f) g) x b) x g) b) c) h) x x x x x 2 h) c) x x i) d) x x 8 d) i) j) x x x 2 e) x 2 e) x 5) j)
Gold: Multiply two to four surd terms together and then simplify Question 8: By only multiplying terms, expand and un-simplify creating 3 or 4 surd terms e.g. Question 7: Multiply and Simplify e.g. x x = 2 2 = x x x X a) a) b) x x b) c) c) x x x - d) 136 - x x x - d) e) e) x x x
Gold: Multiply two to four surd terms together and then simplify ANSWERS Question 6: By only multiplying terms, expand using surds in all your terms. e.g. Question 5: Multiply e.g. = x x = )3 x )2 a) f) f) a) g) )3 x b) )2 g) b) )2 x h) c) x h) c) )4 x d) i) x d) i) e) )2 x j) )3 e) j) Ask a partner to check any alternative solutions to these problems
Gold: Multiply two to four surd terms together and then simplify ANSWERS Question 8: By only multiplying terms, expand and un-simplify creating 3 or 4 surd terms e.g. Question 7: Multiply and Simplify e.g. x x = 2 2 = x x There are lots of possible solutions to these questions so ask a partner to switch with you and assess each other’s solutions. a) a) b) 280 b) c) c) d) d) e) e)
