TCAP 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

8.NS.A.1 Know that numbers that are not rational are called irrational
8.NS.A.2 Use rational approximations of irrational numbers
8.NS.A.3 Estimate values of irrational numbers

Standards basis

Tennessee Academic Standards for Mathematics — Tennessee

How the TCAP reports it

TCAP math is Tennessee’s state assessment program and its blueprints are aligned to Tennessee Academic Standards, which closely mirror the Common Core content structure in grades 3-8 and the CCSS-style high school conceptual categories. The blueprint page lists the current 2025-26 assessment overviews, including Math Grade 2, Grades 3-5, Grades 6-8, and Math EOC. [Tennessee Department of Education](https://www.tn.gov/education/districts/lea-operations/assessment/tcap-blueprints.html)

Blueprint & weighting

Published TCAP math blueprints assign content emphasis by grade/course, but the exact percentage table was not recoverable from the accessible blueprint page in this session. The state blueprint landing page confirms the math overviews but did not expose the PDF links in the fetched page content. [Tennessee Department of Education](https://www.tn.gov/education/districts/lea-operations/assessment/tcap-blueprints.html)

Official sources

Tennessee Department of Education TCAP Blueprints
Tennessee Education Glossary (academic standards entry)

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

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 $\sqrt{2}$ ?

$\sqrt{2} \approx 1.414$ .

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 $11$ .

Keep practicing

Turn the number system into game time.

The TCAP 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 TCAP grades

Grade 6 Grade 7

The same skills on other tests

i-Ready AASA ACAP ATLAS

Source and test overview

All TCAP prep Official test source

Reporting categories

More Grade 8 domains

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