Multiplying and Dividing Surds Slideshow 7, Mr Richard Sasaki, Room 307

Objectives Learn (or review) how to write recurring decimal numbers as fractionsLearn (or review) how to write recurring decimal numbers as fractions Learn how to multiply and simplify numbers in surd formLearn how to multiply and simplify numbers in surd form Learn how to divide and simplify numbers in surd formLearn how to divide and simplify numbers in surd form

Recurring Decimal Numbers A recurring decimal number is a number where decimal digits repeat themselves in a pattern. This pattern continues infinitely. We know how some of these numbers convert to fractions. But some numbers we may need to do calculations to write them as fractions.

Recurring Decimal Numbers If we multiply this number by 10 and then subtract the original (multiply by 9), the recurring digit will disappear. Example

Recurring Decimal Numbers Example To remove recurrence, what should we multiply it by?

Recurring Decimal Numbers Note: The 4 doesn’t recur. Example

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Surd Laws Last lesson, we learned how to simplify surds. The primary rule we learned was: This is, of course useful for multiplying surds. Example So typically, we combine the surds and then simplify it as one expression. This is normally the easiest method.

Surd Laws Example Let’s separate it into four chunks and then combine them. So you may use the fact…

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Dividing Roots How do we divide square roots? If we square both sides, we get… If we square root both sides, we get…

Dividing Roots Dividing surds is often similar to multiplying them. Example If the numbers are kind to you, the question is easy.

Dividing Roots When we divide, the number being rooted may become a fraction. Example We always need an integer as the denominator. If we square the surd denominator, it will become an integer.

Answers - Easy

Answers - Hard