Any expression involving an nth root can be written using radical notation. The symbol is called the radical symbol.
If n is a positive integer and a is a real number for which a1/n is defined, then the expression is called a radical, and
The number a is called the radicand. The number n is called the index of the radical. Radicals of index 2 and 3 are referred to as â€œsquare rootsâ€ and â€œcube roots,â€ respectively, whereas the expression is â€œthe nth root of a.â€ The index 2 is usually omitted. We write rather than . Remember that is simply another notation for a1/n. So is the positive nth root of a when n is even and a is positive, whereas is the real nth root of a when n is odd and a is any real number. The expressions
are not real numbers because there are no even roots of negative numbers in the real number system.
Write each exponential expression using radical notation and each radical expression using exponential notation. Assume the variables represent positive numbers. Do not simplify.
We can write either the root or the power first.
Simplifying radical expressions