Surds and Indicies Flashcards
What are surds?
A way to precisely write a irrational number
RootA x RootB =?
RootAB
RootA/Rootb =?
RootA/B
RooatA + RootB =?
Does not work
RootA - RootB =?
Does not work
RootA +RootA =?
2RootA
2RootA-RootA =?
RootA
How do you simplify surds?
- Find 2 factors that go into the rooted number - one being the largest perfect square which goes into it.
- Re write the surd as the two factors multiplied together - e.g. RootZxY
- Root the factor which is the perfect square out.
- This should leave you with an interger on the outside, multiplying a surd.
Can you collect surds with the same base?
Yes as they are like terms.
How do you rationalise a fraction with a surd as the denominator? ( In this form - 10/3Root3)
Multiply both the numerator and denominator by the surd in the denominator.
How do you rationalise a fraction with a surd on the denominator in this form - 10/5 + Root5?
Multiply both the numerator and denominator by the whole denominator, however change the plus or minus sign to the opposite - to allow the root to be cancelled out (the difference of 2 squares rule)
What are indicies?
The number that is the power to something else - e.g. 2^5
a^m x a^n =
a^m+n
a^m/a^n =
a^m-n
a^0 =
1
a^-m =
1/a^m
a^1/n =
RootA
a^3/n
nRootA^3
(a^m)^n
a^m x n
(a x b)^n
a^n x b^n
How do you simplify sums and differences of fractional powers?
- Write the whole equation in a common simplified form - e.g in (a^m)^n or surd form.
- Factor out any common factor.
- Then continue simplifying until in most common form.
What index is used for Deka
1
What index is used for Hecto
2
What index is used for Kilo
3
What index is used for Mega
6
What index is used for Giga
9
What index is used for Tera
12
What index is used for Peta
15
What index is used for Deci
-1
What index is used for Centi
-2
What index is used for Milli
-3
What index is used for Micro
-6
What index is used for Nano
-9
What index is used for Pico
-12
What index is used for Femto
-15
