RISE Grade 8 The Number System. Practice it free.

Know that there are numbers that are not rational and approximate them by rational numbers. This Grade 8 reporting domain maps to 1 practice skill and 8 representative questions from the playable bank.

Grade 81 mapped skills

What the test measures

The Number System skills

Know that there are numbers that are not rational and approximate them by rational numbers

Standards basis

Utah Core Standards for Mathematics (CCSS-aligned Utah math standards) — Utah

How the RISE reports it

Utah’s RISE mathematics assessment is a state assessment aligned to Utah Core Standards rather than a separately branded national framework. The official Utah pages point to Utah Core standards resources and the RISE administration guidance, with no separate public math blueprint published on the assessment page itself.

Blueprint & weighting

RISE mathematics weighting by domain was not located on the official Utah assessment page; the official page only points to the RISE assessment overview/administration resources and the Utah Core Standards resources. Grade 6 administration guidance notes a two-segment math test with Segment 1 no calculator and Segment 2 calculator allowed, and the proctor guide states Mathematics has an expected testing time of 90 minutes for most students and 135 minutes for all students.

Official sources

Utah State Board of Education Assessments
Utah State Board of Education Learning Resources for Families
Utah State Board of Education Assessment Contacts PDF

Practice by skill

Topics mapped to this domain

Irrational number approximations

Grade 820 questions

Try it now

8 free questions · 0/0 correct

Practice playeasy

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

$\sqrt{3} \approx 1.732$ .

Practice playeasy

Which is closest to $\sqrt{5}$ ?

$\sqrt{5} \approx 2.236$ .

Practice playeasy

$\sqrt{40}$ is between two consecutive integers. Enter the smaller one.

$6^2 = 36 < 40 < 49 = 7^2$ , so $\sqrt{40}$ is between $6$ and $7$ ; the smaller is $6$ .

Practice playeasy

$\sqrt{27}$ lies between two consecutive integers. Enter the larger one.

$5^2 = 25 < 27 < 36 = 6^2$ , so $\sqrt{27}$ is between $5$ and $6$ ; the larger is $6$ .

Practice playeasy

What integer is closest to $\sqrt{120}$ ?

$11^2 = 121$ sits right above $120$ and $\sqrt{120} \approx 10.95$ , so the closest integer is $11$ .

Practice playeasy

What is the integer part of $\sqrt{10} + 2$ ?

$\sqrt{10} \approx 3.16$ , so $\sqrt{10} + 2 \approx 5.16$ ; the integer part is $5$ .

Practice playeasy

Which is closest to $\pi$ ?

$\pi \approx 3.14159$ .

Practice playeasy

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

$\sqrt{2} \approx 1.414$ .

Keep practicing

Turn the number system into game time.

The RISE 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

The Number System in other RISE grades

Grade 6 Grade 7

The same skills on other tests

i-Ready AASA ACAP ATLAS

Source and test overview

All RISE prep Official test source

Reporting categories

More Grade 8 domains

Expressions and EquationsWork with radicals and integer exponents, analyze and solve linear equations and pairs of simultaneous linear equations.8 QsPractice →FunctionsDefine, evaluate, and compare functions; use functions to model relationships between quantities.8 QsPractice →GeometryUnderstand and apply the Pythagorean theorem, and solve problems involving similarity and congruence.8 QsPractice →Statistics and ProbabilityInvestigate patterns of association in bivariate data.8 QsPractice →