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Multiplying and Dividing Surds. Slideshow 7, Mr Richard Sasaki, Room 307. Objectives. Learn (or review) how to write recurring decimal numbers as fractions Learn how to multiply and simplify numbers in surd form Learn how to divide and simplify numbers in surd form.
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Multiplying and Dividing Surds Slideshow 7, Mr Richard Sasaki, Room 307
Objectives • Learn (or review) how to write recurring decimal numbers as fractions • Learn how to multiply and simplify numbers in surd form • Learn 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 For a number like , just one digit repeats (the 7). We need to change this number to get rid of the recurring symbol. If we multiply this number by 10 and then subtract the original (multiply by 9), the recurring digit will disappear. Example Write as a fraction. Let .
Recurring Decimal Numbers If we have more than a group of digits with recurring symbols (eg: ), those digits repeat in that sequence. (eg: 0.374374374374…) Example Writeas a fraction. Let . To remove recurrence, what should we multiply it by?
Recurring Decimal Numbers The multiplication process differs with numbers where the first recurring digit isn’t in the tenths position (eg: Example Note: The 4 doesn’t recur. Write as a fraction. Let .
Surd Laws Last lesson, we learned how to simplify surds. The primary rule we learned was: , where . This is, of course useful for multiplying surds. Example Simplify . So typically, we combine the surds and then simplify it as one expression. This is normally the easiest method.
Surd Laws Of course, surds are often in the form where . Example Simplify . Let’s separate it into four chunks and then combine them. Lastly, let’s simplify . So you may use the fact… for .
Dividing Roots How do we divide square roots? Let’s consider two roots, and where . If we square both sides, we get… If we square root both sides, we get… , where .
Dividing Roots Dividing surds is often similar to multiplying them. Example Calculate and simplify . Calculate and simplify . 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 Calculate and simplify . We always need an integer as the denominator. When you write a fraction, it must be in the form where . If we square the surd denominator, it will become an integer.
