Question

Below are statements about radicals and rational exponents. Which of the statements are true? Check all that apply. The nth root of ____ can be written as ____ and as the notation ____ is rational exponent notation for the square root of ____. The notation ____ is radical notation for the square root of ____.

1) The nth root of a can be written as a^(1/n)
2) The notation a^(1/2) is rational exponent notation for the square root of a
3) The notation sqrt(a) is radical notation for the square root of a
4) The nth root of a can be written as a^(n/1)
5) The notation a^(1/2) is radical notation for the square root of a

Answer 1

The nth root of a can be written as a^(1/n), a^(1/2) is equivalent to the square root of a, and sqrt(a) represents the square root of a.

Step-by-step explanation:

The true statements about radicals and rational exponents are:

1. The nth root of a can be written as a^(1/n): When we want to express the nth root of a number, we can write it as a to the power of 1/n. For example, the cube root of 8 can be written as 8^(1/3).
2. The notation a^(1/2) is rational exponent notation for the square root of a: When we have an exponent of 1/2, it represents the square root of a number. So a^(1/2) is equivalent to the square root of a.
3. The notation sqrt(a) is radical notation for the square root of a: The square root of a number can be represented using radical notation as sqrt(a).