cube root

(noun)

A root of degree 3, written in the form $\sqrt[3]{a}$.

Related Terms

Examples of cube root in the following topics:

  • Radical Functions

    • An expression with roots is called a radical function, there are many kinds of roots, square root and cube root being the most common.
    • The cube root of a number ($\sqrt [ 3 ]{x}$ ) can also be taken.
    • The cube root is the number which, when cubed, or multiplied by itself and then multiplied by itself again, gives back the original number.
    • For example, the cube root of 8 is 2 because $2 \cdot 2\cdot 2=8$ , or $\sqrt[3]{8}=2$
    • Irrational numbers also appear when attempting to take cube roots or other roots.

  • Introduction to Radicals

    • Roots are the inverse operation of exponentiation.
    • For now, it is important simplify to recognize the relationship between roots and exponents: if a root $r$ is defined as the $n \text{th}$ root of $x$, it is represented as
    • The cube root of a number ($\sqrt [ 3 ]{x}$ ) can also be calculated.
    • The cube root of a value $x$ is the number that when cubed (i.e., when raised to an exponent of 3) yields the original number $x$.
    • For example, the cube root of 8 is 2 because $2^3 = 2 \cdot 2\cdot 2=8$.

  • Simplifying Radical Expressions

    • Expressions that include roots are known as radical expressions.
    • where $n$ is the degree of the root.
    • A root of degree 2 is called a square root and a root of degree 3, a cube root.
    • Roots of higher degrees are referred to using ordinal numbers, as in fourth root, twentieth root, etc.
    • First, look for a perfect square under the square root sign and remove it:

  • Additional Measures of Central Tendency

    • The geometric mean is computed by multiplying all the numbers together and then taking the nth root of the product.
    • Since there are three numbers, we take the cubed root of the product (1,000) which is equal to 10.
    • Raising a value to the 1/Nth power is, of course, the same as taking the Nth root of the value.
    • In this case, 10001/3 is the cube root of 1,000.

  • Radical Equations

    • When solving equations that involve radicals, begin by asking: is there an x under the square root?
    • If there is an $x$, or variable, under the square root, the problem must be approached differently.
    • Square both sides of the equation if the radical is a square root; Cube both sides if the radical is a cube root.
    • To undo the radical symbol (square root), square both sides of the equation.
    • $(\sqrt{6x-2})^2=(10)^2$,  squaring a square root leaves the expression under the square root symbol and $10$ squared is $100$

  • Mean: The Average

    • The geometric mean is defined as the $n$th root (where $n$ is the count of numbers) of the product of the numbers.
    • For instance, the geometric mean of two numbers, say 2 and 8, is just the square root of their product; that is $\sqrt{2\cdot8} = 4$.
    • As another example, the geometric mean of the three numbers 4, 1, and 1/32 is the cube root of their product (1/8), which is 1/2; that is $\sqrt[3]{4\cdot 1 \cdot \frac{1}{32}} = \frac{1}{2}$.

  • Root Modifications

    • There are many different types of specialized roots, but two of the more familiar types of roots include aerial roots and storage roots.
    • Storage roots (for example, taproots and tuberous roots) are modified for food storage.
    • Epiphytic roots are a type of aerial root that enable a plant to grow on another plant in a non-parasitic manner.
    • The epiphytic roots of orchids develop a spongy tissue to absorb moisture and nutrients from any organic material on their roots.
    • Other examples of modified roots are aerating roots and haustorial roots.

  • The Evolution of Roots in Seedless Plants

    • A tap root system has a main root that grows down vertically from which many smaller lateral roots arise.
    • In addition, some plants actually have a combination of tap root and fibrous roots.
    • The tip of the root is protected by the root cap, a structure exclusive to roots and unlike any other plant structure.
    • Aerial roots and prop roots are two forms of aboveground roots that provide additional support to anchor the plant.
    • (a) Tap root systems have a main root that grows down, while (b) fibrous root systems consist of many small roots.

  • Types of Root Systems and Zones of Growth

    • Dicots have a tap root system, while monocots have a fibrous root system, which is also known as an adventitious root system.
    • A tap root system has a main root that grows down vertically, from which many smaller lateral roots arise.
    • Some plants have a combination of tap roots and fibrous roots.
    • The tip of the root is protected by the root cap, a structure exclusive to roots and unlike any other plant structure.
    • (a) Tap root systems have a main root that grows down, while (b) fibrous root systems consist of many small roots.

  • Logarithmic Functions

    • For example, the third power (or cube) of 2 is 8, because 8 is the product of three factors of 2: $2^{3} = 2 \times 2\times 2 = 8$.
    • For the definition to work, it must be understood that ' raising two to the 0.3219 power' means 'raising the 10000th root of 2 to the 3219th power'.
    • The tenthousandth root of 2 is 1.0000693171 and this number raised to the 3219th power is 1.2500, therefore ' 2 multiplied by itself 3.3219 times' will be 2 x 2 x 2 x 1.2500 namely 10.