Problem preview

N-RN.1 Warmup M2-060-A09-V01

Explain rational exponents as extensions of integer exponent rules and as radical notation.

Interpret a rational exponent's rooted quantity and dimension

Problem

Interpret the rational exponent in \(s~=~A^{1/2}\), where \(A\) is the area of a square.

Neutral reference: A is the area of a square, s is its side length, and the student is asked to interpret s equals A to the one-half power.

Big Picture

What this problem is really about

The one-half power reverses the square relationship between a square’s side and area. We’ll write the area formula, interpret the exponent as a principal square root, explain why the geometric length is nonnegative, and track squared-length units through the root to recover ordinary length units.

Answer choices

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Take the square root of side length s to recover another side length.

Divide area A by 2 to obtain s.

Square area A to obtain s.

Take the square root of area A to recover side length s; (length²)¹/² has length units.

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Curriculum context

Course: Math II
Standard: N-RN.1
Category: Number and Quantity
Domain: The Real Number System
Objective: Explain rational exponents as extensions of integer exponent rules and as radical notation.
Problem type: Interpret a rational exponent's rooted quantity and dimension