Finding Cube Roots of Rational Numbers
Grade 8 math students learn to find cube roots of rational numbers, including integers, fractions, and decimals. For integers, prime factorization reveals the three identical groups forming the cube root. For fractions, the cube root of a/b equals the cube root of a divided by the cube root of b. Covered in Big Ideas Math, Course 3, Chapter 7: Real Numbers and the Pythagorean Theorem.
Key Concepts
To find the cube root of a perfect cube integer, you can use its prime factorization. For a fraction, the cube root of the quotient is the quotient of the cube roots: $$\sqrt[3]{\frac{a}{b}} = \frac{\sqrt[3]{a}}{\sqrt[3]{b}}$$.
Common Questions
How do you find the cube root of an integer?
Use prime factorization to break the number into prime factors. Group them into three identical sets. The product of one set is the cube root. For example, cube root of 216 = 6 because 216 = 6^3.
How do you find the cube root of a fraction?
Apply the property: cube root of (a/b) = cube root of a / cube root of b. Find the cube root of numerator and denominator separately. For example, cube root of (-8/125) = -2/5.
How do you find the cube root of a decimal?
Convert the decimal to a fraction first, then apply the quotient property for cube roots. For example, cube root of 0.027 = cube root of (27/1000) = 3/10 = 0.3.
Which textbook covers cube roots for Grade 8?
This topic is in Big Ideas Math, Course 3, Chapter 7: Real Numbers and the Pythagorean Theorem.
What grade level covers cube roots?
Finding cube roots of rational numbers is typically covered in Grade 8 math.