nth Roots
nth Roots is a Grade 7/intermediate algebra skill in Yoshiwara Intermediate Algebra, Chapter 6: Powers and Roots. Students learn to evaluate nth roots including square roots, cube roots, and higher roots, understanding the inverse relationship between raising to a power and taking the corresponding root.
Key Concepts
Property $s$ is called an $n$th root of $b$ if $s^n = b$. We use the symbol $\sqrt[n]{b}$ to denote the $n$th root of $b$. An expression of the form $\sqrt[n]{b}$ is called a radical, $b$ is called the radicand, and $n$ is called the index of the radical.
Examples $\sqrt[3]{27} = 3$ because $3^3 = 27$.
$\sqrt[4]{256} = 4$ because $4^4 = 256$.
Common Questions
What is an nth root?
The nth root of a number a is a value b such that b raised to the nth power equals a. Written as the nth root of a or a to the power 1/n.
What are some examples of nth roots?
The square root of 25 is 5 (since 5 squared equals 25). The cube root of 27 is 3 (since 3 cubed equals 27). The 4th root of 16 is 2 (since 2 to the 4th equals 16).
How is the nth root related to exponents?
Taking the nth root is the inverse of raising to the nth power. The nth root of a equals a to the power of 1/n.
Can you take even roots of negative numbers?
No. Even roots of negative numbers are not real numbers. You cannot find a real square root of negative 4, for example. Odd roots of negative numbers are real.
What chapter covers nth roots in Yoshiwara Intermediate Algebra?
nth Roots are covered in Chapter 6: Powers and Roots in Yoshiwara Intermediate Algebra.