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41.
Power of a root
$\left(\sqrt[n]{a}\right)^m=\sqrt[n]{a^m}$
Root
42.
Rationalize fractions
$\dfrac{1}{\sqrt[n]{a}}= \dfrac{\sqrt[n]{a^{n-1}}}{a}$
Root
43.
Root of a product
$\sqrt{ab}=\sqrt{a}\sqrt{b}$
Square root
44.
Root of a fraction
$\sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}$
Square root
45.
Root of a square
$\sqrt{a^2} = |a|$
Square root
46.
Square of a root
$\left(\sqrt{a}\right)^2=a$
Square root
47.
Rationalise denominator
$\dfrac{1}{\sqrt{a}}=\dfrac{\sqrt{a}}{a}$
Square root
48.
Rationalise denominator
$\dfrac{1}{\sqrt{a}+\sqrt{b}}=\dfrac{\sqrt{a}-\sqrt{b}}{a-b}$
Square root
49.
Rationalise denominator
$\dfrac{1}{\sqrt{a}-\sqrt{b}}=\dfrac{\sqrt{a}+\sqrt{b}}{a+b}$
Square root
50.
Lagrange's Identity
$\sqrt{a \pm \sqrt{b}}=\dfrac{\sqrt{a+\sqrt{a^2-b}}}{2} \pm \dfrac{\sqrt{a-\sqrt{a^2-b}}}{2}$
Square root
51.
Definition of logarithm
$\log_ba=x \iff b^x=a$
Logarithm
52.
Log of 1
$\log_a 1=0$
Logarithm
53.
Log of same numbers
$\log_a a = 1$
Logarithm
54.
Product rule for logarithms
$\log_a {xy}=\log_a x + \log_a y$
Logarithm
55.
Quotient rule for logarithms
$\log_a \dfrac{x}{y} = \log_ax - \log_ay$
Logarithm
56.
Power rule for logarithms
$\log_ax^n=n\log_ax$
Logarithm
57.
Log of square root
$\log_a\sqrt[n]{x}=\dfrac{1}{n} \log_ax$
Logarithm
58.
Change of base
$\log_ba=\dfrac{\log_ax}{\log_ay}$
Logarithm
59.
Change of base
$\log_ax=\dfrac{1}{\log_xa}$
Logarithm
60.
$a^{\log_ax}=x$
Logarithm

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