User:
• Matrices
• Algebra
• Geometry
• Graphs and functions
• Trigonometry
• Coordinate geometry
• Combinatorics
 Suma y resta Producto por escalar Producto Inversa
 Monomials Polynomials Special products Equations Quadratic equations Radical expressions Systems of equations Sequences and series Inner product Exponential equations Matrices Determinants Inverse of a matrix Logarithmic equations Systems of 3 variables equations
 2-D Shapes Areas Pythagorean Theorem Distances
 Graphs Definition of slope Positive or negative slope Determine slope of a line Equation of a line Equation of a line (from graph) Quadratic function Parallel, coincident and intersecting lines Asymptotes Limits Distances Continuity and discontinuities
 Sine Cosine Tangent Cosecant Secant Cotangent Trigonometric identities Law of cosines Law of sines
 Equations of a straight line Parallel, coincident and intersecting lines Distances Angles in space Inner product

Cube Roots

# Cube root of perfect cubes

The product of the same three factors is called a perfect cube.

For example,
1 is a perfect cube because 1=1x1x1=13
8 is a perfect cube because 8=2x2x2=23
27 is a perfect cube because 27=3x3x3=33
64 is a perfect cube because 64=4x4x4=43
...

The cube root of a number is the opposite (or inverse) of cubing a number.

$\sqrt[3]{64}=4$     because 4x4x4=64

$\sqrt[3]{125}=5$     because 5x5x5=125

To find the cube root of a fraction, reduce the numerator and the denominator to perfect cubes is possible.

Find $\sqrt[3]{\frac{16}{250}}$

$\sqrt[3]{\frac{16}{250}}=\sqrt[3]{\frac{8}{125}}=\frac{\sqrt[3]{8}}{\sqrt[3]{125}}=\frac{2}{5}$

Find $\sqrt[3]{5\frac{23}{64}}$

$\sqrt[3]{5\frac{23}{64}}=\sqrt[3]{\frac{343}{64}}=\frac{\sqrt[3]{343}}{\sqrt[3]{64}}=\frac{7}{4}=1\frac{3}{4}$

Find $\sqrt[3]{64}$

Solution: