Cube Root Definition and Notation
Cube root definition and notation is a Grade 7 math concept in Big Ideas Math Advanced 2, Chapter 7: Real Numbers and the Pythagorean Theorem. The cube root of a is the number b such that b cubed equals a, written with the cube root symbol. Unlike square roots, every real number including negatives has a real cube root — the cube root of negative 8 is negative 2.
Key Concepts
$b$ is the cube root of $a$ if $b$ cubed equals $a$. In symbols, we write $$b = \sqrt[3]{a} \quad \text{if} \quad b^3 = a$$ Unlike square roots, which are not real for negative numbers, every real number has a real cube root.
Common Questions
What is a cube root?
The cube root of a number a is the value b such that b times b times b equals a. For example, the cube root of 27 is 3 because 3 times 3 times 3 equals 27.
Can you take the cube root of a negative number?
Yes, unlike square roots, cube roots of negative numbers are real. The cube root of negative 8 is negative 2 because negative 2 times negative 2 times negative 2 equals negative 8.
What is the relationship between cubing and cube roots?
Cubing a number and taking a cube root are inverse operations. Cubing 4 gives 64, and taking the cube root of 64 gives back 4.
What textbook covers cube root definition in Grade 7?
Big Ideas Math Advanced 2, Chapter 7: Real Numbers and the Pythagorean Theorem covers the definition and notation of cube roots.