Simplifying & Roots
What is the assumed index if a radical expression is written without one?
2 (square root)
What two characteristics must a radical share before you can combine the coefficients using addition or subtraction?
The index and radicand.
What is the general exponential form of the radical expression root(n)(a)
a^((1)/(n))
Given f(x) = a root(n)(x-h) + k a positive 'h' corresponds to what shift?
Italian mathematician Leonardo of Pisa (known as Fibonacci) found a sequence called the Fibonacci Sequence. In his 1202 book, Liber Abaci he used it to solve a problem about the growth of a hypothetical population of which animal?
What is the name of the number or expression located under the radical sign? E.g.
root(n)(a^m)
Radicand
What is the name of the rule that allows for the following relationship to be true:
root(n)(a) cdot root(n)(b) = root(n)(ab)
The Product Rule
What two expressions are equivalent to the rational exponent a^((m)/(n))
root(n)(a^m) and
(root(n)(a))^m
What is the name of the graph test used to determine whether the inverse of a relation is a function?
The Horizontal Line Test
What is the only even prime number?
2, it is prime.
In order to perfectly simplify a variable
root(n)(a^m)
the exponent of the variable must be a multiple of what value?
The index (n)
What expression should be used in the numerator and denominator when rationalizing a fraction with the denominator:
sqrt(6)-sqrt(2)
The conjugate:
sqrt(6) + sqrt(2)
What is the simplified form of the following expression:
x^(1/2) cdot x^(3/2)
x^2
What is the final step: 1) Replace f(x) with y, 2) interchange x and y, 3) solve for y, and then what?
Replace y with
f^-1(x)
Snowflakes exhibit a rotational symmetry(they are symmetric about a point), this is due to the water (H2O), as a result of this which amount of rotational symmetry does it exhibit? (Hint: 2 fold, 4 fold, 6 fold etc.)
Six fold symmetry (Hexagonal)
When dividing radicals the first step is to divide which specific terms?
The coefficients! (You can also simplify before solving anyway)
Simplify the following expression:
(7sqrt(x^3y^4))/(sqrt(64x^2y^3)
(7ysqrt(x))/(8sqrt(y))
Given the following expressions, write a new expression h(x)=f(x)+g(x) :
f(x) = sqrt(x-8) + 2
g(x) = x^2+8
h(x)=sqrt(x-8)+2+x^2+8
This is the famous problem that Leonhard Euler (yes the same as the number e) solved in 1736. It became foundational to the mathematics of graph theory. What were the names of the bridges that were in the problem?
The Bridges of Konigsberg.
Simplify the following radical expression:
sqrt(875(
5 sqrt(35)
What is the product of the following:
(sqrt(5)-sqrt(3))(sqrt(5)+sqrt(3))
2
Simplify the following
m^(7/4)/sqrt(m^5)
1/root(4)(m^3)
A function f and a function g are inverse functions if and only if what condition(s) is/are met?
If f(g(x)) = x and g(f(x)) = x then they are inverses.
What trick did mathematicians use to approximate the circumference of circles before they could identify the ratio pi?
They used inscribed polygons (squares, pentagons, octagons, etc.) and found their perimeter.