Standards and Objectives for Radicals, Exponents, and Irrational Numbers

Vocabulary terms and standard definitions covering irrational numbers, square and cube roots, and exponents based on the classroom learning standards.

Standard 8.NR.1.2

The standard requiring students to approximate irrational numbers to compare their size, locate them approximately on a number line, and estimate the value of expressions.

Standard 8.NR.2

The standard focused on solving problems involving radicals and integer exponents, applying place value understanding with scientific notation, and using scientific notation to explain real phenomena.

Standard 8.NR.2.2

The standard requiring the use of square root and cube root symbols to represent solutions to equations, recognizing the number of solutions for equations of the form $x^2 = p$ and $x^3 = p$, and evaluating square roots of perfect squares and cube roots of perfect cubes.

Solutions to $x^2 = p$

An equation that has two solutions, where $p$ is a positive rational number.

Solutions to $x^3 = p$

An equation that has one solution, where $p$ is a positive or negative rational number.

Evaluation range for perfect squares (8.NR.2.2)

Square roots of perfect squares up to and including $625$.

Evaluation range for perfect cubes (8.NR.2.2)

Cube roots of perfect cubes greater than or equal to $-1000$ and less than or equal to $1000$.