MAST Grade 8 Understand and Use Irrational Numbers. Practice it free.

Students approximate irrational numbers and solve equations involving square roots and cube roots. This Grade 8 reporting domain maps to 4 practice skills and 8 representative questions from the playable bank.

Grade 8Testlet 14 mapped skills

What the test measures

Understand and Use Irrational Numbers skills

Approximate the value of irrational numbers and use irrational numbers to solve problems.
Solve equations with square roots and cube roots.
Standards: 8.NS.1, 8.NS.2, 8.EE.2, 8.G.9

Standards basis

Montana PK-12 Mathematics Content Standards / Common Core State Standards for Mathematics (CCSS-M)-aligned Montana standards — Montana

How the MAST reports it

Montana’s MAST is a state-specific through-year assessment built by New Meridian and aligned to Montana’s academic content standards, not a Smarter Balanced-style claims/targets framework. The math blueprints organize content into grade-level strands/testlets that map directly to CCSS-M-derived Montana standards.

Blueprint & weighting

The blueprint publishes a through-year design of 12 strands/testlets per grade, with 1 strand per testlet, 2 reporting attributes per strand, and 9–13 items per testlet. It also specifies approximate item-type and DOK distributions, but does not publish percentage weighting by domain in the captured blueprint text.

Official sources

Montana OPI MontCAS
Montana OPI - MasteryGuide Mathematics Assessment Specifications and Blueprints
Montana OPI - Montana MAST Math Testlets

Practice by skill

Topics mapped to this domain

Volume of prisms and cylinders

Grade 731 questions

Irrational number approximations

Grade 840 questions

Square and cube equations (ACT/SAT)

Grade 815 questions

Square roots and cube roots

Grade 821 questions

Try it now

8 free questions · 0/0 correct

Practice playeasy

A rectangular prism has length $2$ , width $5$ , and height $6$ . What is its volume?

$V = 2 \times 5 \times 6 = 60$ .

Practice playeasy

Which is closest to $\sqrt{2}$ ?

$\sqrt{2} \approx 1.414$ .

Practice playeasy

Solve for all values of $x\textsf{.}$

$x^{2} = 225$

$15 \times 15 = 225$ and $(-15) \times (-15) = 225\textsf{,}$ so $x = \pm 15\textsf{.}$

Practice playeasy

Solve for the positive value of $x$ : $x^2 = 121$ .

$x = \sqrt{121} = 11$ because $11 \times 11 = 121$ .

Practice playeasy

A cylinder has radius $2$ and height $3$ . Using $\pi = 3$ , what is its volume?

$V = \pi r^2 h = 3 \times 4 \times 3 = 36$ .

Practice playeasy

Which is closest to $\sqrt{3}$ ?

$\sqrt{3} \approx 1.732$ .

Practice playeasy

Solve for all values of $x\textsf{.}$

$x^{2} = 400$

$20 \times 20 = 400$ and $(-20) \times (-20) = 400\textsf{,}$ so $x = \pm 20\textsf{.}$

Practice playeasy

What is $\sqrt{81}$ ?

$9 \times 9 = 81$ , so $\sqrt{81} = 9$ .

Keep practicing

Turn understand and use irrational numbers into game time.

The MAST placement starts with this test's real coverage map and finds the right difficulty.

Batting Cage game cover

Batting CagePlay →

Blaster Gate game cover

Blaster GatePlay →

Blitz Tanks game cover

Blitz TanksPlay →

Buzzer Beater game cover

Buzzer BeaterPlay →

Related Common Core standards

7.G.B.6 8.G.C.9 8.NS.A.2 8.EE.A.2

Source and test overview

All MAST prep Official test source

Reporting categories

More Grade 8 domains

Exponent Rules and Scientific NotationStudents apply rules of exponents and use scientific notation to solve problems.8 QsPractice →Construct FunctionsStudents construct a function and interpret and analyze function components.8 QsPractice →Linear Equations in One VariableStudents recognize different solution types and solve linear equations with rational number coefficients.8 QsPractice →Proportional Relationships and LinesStudents use slope and equations of a line to solve problems and graph proportional relationships.8 QsPractice →Systems of EquationsStudents solve systems of equations algebraically or from verbal descriptions and estimate solutions from graphs.8 QsPractice →Pythagorean TheoremStudents use the Pythagorean Theorem to find side lengths and distance in the coordinate plane.8 QsPractice →