NJSLA 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 8NS1 mapped skills
What the test measures

The Number System skills

  1. 8.NS.A.1 Know that numbers that are not rational are called irrational

  2. 8.NS.A.2 Use rational approximations of irrational numbers

Standards basis

New Jersey Student Learning Standards for Mathematics (NJSLS-M), aligned to Common Core State Standards for Mathematics (CCSS-M) — New Jersey

How the NJSLA reports it

NJSLA math is built on the New Jersey Student Learning Standards for Mathematics, which closely follow the Common Core domain structure and progressions. The assessment is organized by grade-level and end-of-course reporting aligned to those standards rather than by a separate proprietary framework.

Blueprint & weighting

NJDOE publishes statewide assessment administration information and grade/course coverage, but no official public math-domain weighting blueprint was located in the retrieved primary materials.

Practice by skill

Topics mapped to this domain

Irrational number approximations

Grade 840 questions
Try it now

8 free questions · 0/0 correct

Practice playeasy

Which is closest to 3\sqrt{3}?

3≈1.732\sqrt{3} \approx 1.732.

Practice playeasy

Which is closest to 5\sqrt{5}?

5≈2.236\sqrt{5} \approx 2.236.

Practice playeasy

Between which two consecutive integers does 40\sqrt{40} lie?

62=366^{2} = 36 and 72=49.7^{2} = 49\textsf{.} Since 36<40<49,36 < 40 < 49\textsf{,} 40\sqrt{40} is between 66 and 7.7\textsf{.}

Practice playeasy

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

52=25<27<36=625^2 = 25 < 27 < 36 = 6^2, so 27\sqrt{27} is between 55 and 66; the larger is 66.

Practice playeasy

What integer is closest to 83\sqrt{83}?

92=819^2 = 81 is very close to 8383 and 83≈9.1\sqrt{83} \approx 9.1, so the closest integer is 99.

Practice playeasy

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

10≈3.16\sqrt{10} \approx 3.16, so 10+2≈5.16\sqrt{10} + 2 \approx 5.16; the integer part is 55.

Practice playeasy

Which is closest to π\pi?

π≈3.14159\pi \approx 3.14159.

Practice playeasy

Which is closest to 2\sqrt{2}?

2≈1.414\sqrt{2} \approx 1.414.

Keep practicing

Turn the number system into game time.

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

Batting Cage game coverBatting CagePlay →Blaster Gate game coverBlaster GatePlay →Blitz Tanks game coverBlitz TanksPlay →Buzzer Beater game coverBuzzer BeaterPlay →
Related Common Core standards
8.NS.A.2
The Number System in other NJSLA grades
Grade 6Grade 7
The same skills on other tests
i-ReadyAASAACAPATLAS
Source and test overview
All NJSLA prepOfficial test source
Reporting categories

More Grade 8 domains

Expressions and EquationsWork with radicals and integer exponents; understand the connections between proportional relationships, lines, and linear equations; 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 congruence and similarity using physical models, transparencies, or geometry software; understand and apply the Pythagorean theorem; solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.8 QsPractice →Statistics and ProbabilityInvestigate patterns of association in bivariate data.8 QsPractice →