surds and indices Flashcards
x^0
1
x^n ÷ x^m
x^n-m
(x^n)^m
x^n*m
x^n * x^m
x^n + m
x^-n
1/x^n
x^n/m
m√ x^n
what is a surd
number that cant be square rooted put into a square root
How to solve non equation surds
Multiply all the denominators to remove the fractions
Then divide again to make a collective fraction
what is the exponential form
the form with a power
what are these properties to simplify surds
1. √ a x √ b = ?
2. √ a / √ b = ?
3. √ a x √ a = ?
- √ ab
- √ a/b
- a
how to simplify a surd √ using 2.
for example √ 27
first u pull out a squarable or cubable(Depending on ur √ ) out from the number
√ 27 = √ 9 x √ 3
u pull 9, this is cuz 9 can be squared
= 3 x √ 3
= 3√ 3
what about rly lengthy questions how do i solve them for surds
u can combo the 3 properties,
1. √ a x √ b = √ ab
2. √ a / √ b = √ a/b
3. √ a x √ a = a
what is a conjugate surd
it js means a surd of opposite signs
The conjugate of √ 2 would be its opposite, which is -√ 2
whnat do conjugate surds always result in
the product of conjugate surds is always a rational number
All real value positive qns
Make into cts form
a(x-h)^2 +k
a(x-h)^2 >= 0 cuz its squared and all squared no. R positive
Hence
a(x-h)^2 +k >= k
