Vocabulary: Radical, Radicand, and Principal Root
Vocabulary: Radical, Radicand, and Principal Root introduces Grade 6 students to the terminology for square roots: the radical sign (√), the radicand (the number inside), and the principal square root (the non-negative square root). Covered in Yoshiwara Elementary Algebra Chapter 5: Exponents and Roots, this vocabulary is essential for correctly reading and writing radical expressions. The principal root convention ensures expressions like √25 have exactly one value (5, not ±5).
Key Concepts
Property The symbol $\sqrt{\ }$ is called a radical sign, and the number inside is called the radicand. The positive square root of a number is called the principal square root.
Examples The principal square root of 81 is written as $\sqrt{81}$, which equals 9. To express the negative square root of 36, we write $ \sqrt{36}$, which equals $ 6$. The expression $\pm\sqrt{100}$ represents both square roots of 100, which means 10 or $ 10$.
Explanation The radical symbol $\sqrt{\ }$ is a specific instruction to find only the positive square root, known as the principal root.
Common Questions
What is a radical sign?
The radical sign (√) is the symbol indicating a square root (or other root). The expression under the radical sign is called the radicand.
What is a radicand?
The radicand is the number or expression under the radical sign. In √16, the radicand is 16.
What is the principal square root?
The principal square root is the non-negative (positive) square root of a number. √25 = 5, not -5, by the principal root convention.
Where is this vocabulary covered in Yoshiwara Elementary Algebra?
Radical, radicand, and principal root are introduced in Chapter 5: Exponents and Roots of Yoshiwara Elementary Algebra.
Why do we use the principal square root?
The principal root convention gives a single, unambiguous value for the radical expression. When both roots are needed, we write ±√.