B. Powers of Roots. Math 10: Foundations and Pre-Calculus. Key Terms:. Find the definition of each of the following terms : Irrational Number Real Number Entire Radical Mixed radical. 1. Remembering how to Estimate Roots. Index tells you what root to take
Math 10: Foundations and Pre-Calculus
Radicals that are square roots of perfect squares, cube roots of perfect squares, and so on are rational numbers
Irrational Numbers, cannot be written in the form m/n, where m and n are integers and n≠0
When an irrational number is written as a radical, the radical is the exact value of the irrational number
We can use the square root and cube root buttons on our calculator to determine the approximate values of these irrational numbers
Together, the rational numbers and irrational numbers form a set of real numbers
We can use this property to simplify roots that are not perfect squares, cubes, etc, but have factors that are perfect squares, cubes, etc.
To write a radical of index n in simplest form, we write the radicand as a product of 2 factors, one of which is the greatest perfect nth power.
In grade 9, you learned that for powers with variable bases and whole number exponents
Raising a number to the exponent ½ is equivalent to taking the square root of the number
A fraction can be written as a terminating or repeating decimal, so we can interpret powers with decimal exponents.
To give meaning to a power such as 82/3, we extend the exponent law.
These examples illustrate that numerator of a fractional exponent represents a power and the denominator represents a root.
We can use the exponent laws to simplify expressions that contain rational bases