NJSLA Algebra I The Real Number System Practice

The Real Number System skills

N-RN.A.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents

N-RN.A.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents

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.

Official sources

New Jersey Department of Education - Assessment
New Jersey Department of Education - 2023 NJSLS-Mathematics
NJDOE - Statewide Assessment Testing Schedule 2026-27

8 free questions · 0/0 correct

Practice playmedium

Which expression is equivalent to $3\sqrt{20}+\sqrt{45}$ ?

$3\sqrt{20}=3\sqrt{4 \cdot 5}=3 \cdot 2\sqrt{5}=6\sqrt{5}$ and $\sqrt{45}=\sqrt{9 \cdot 5}=3\sqrt{5}$ . Adding like radical terms gives $6\sqrt{5}+3\sqrt{5}=9\sqrt{5}$ .

Practice playhard

If $\Large x$ and $\Large y$ are positive, which expression is equivalent to $\Large \sqrt[5]{x^8 y^{12}}$ ?

Divide each exponent by $\Large 5$ : $\Large x^{\tfrac{8}{5}} y^{\tfrac{12}{5}}$ .

Practice playmedium

The diagonal length, in inches, of a certain square television screen can be estimated by multiplying the screen's area, in square inches, by $2$ and then taking the square root of the product. According to this method, what is the estimated diagonal length, in inches, of a screen with an area of $216$ square inches?

The product is $216 \cdot 2 = 432$ . Factor $432 = 144 \cdot 3$ , where $144$ is the largest perfect-square factor. So $\sqrt{432} = \sqrt{144 \cdot 3} = 12\sqrt{3}$ , and $3$ is square-free.

Practice playeasy

Write $\sqrt[5]{x^3}$ as $x^{a/b}$ in lowest terms. What is $b$ ?

$\sqrt[5]{x^3} = x^{3/5}$ , so $b = 5$ .

Practice playeasy

Which expression is equivalent to $\sqrt{288}$ ?

$288 = 144 \cdot 2$ , so $\sqrt{288} = \sqrt{144 \cdot 2} = 12\sqrt{2}$ .

Practice playmedium

Which expression is equivalent to $\sqrt{28}+\sqrt{63}+\sqrt{7}$ ?

$\sqrt{28}=2\sqrt{7}$ , $\sqrt{63}=3\sqrt{7}$ , and $\sqrt{7}=\sqrt{7}$ . Adding gives $2\sqrt{7}+3\sqrt{7}+\sqrt{7}=6\sqrt{7}$ .

Practice playeasy

If $\Large a$ and $\Large b$ are positive, which expression is equivalent to $\Large \sqrt[4]{a^8 b^{12}}$ ?

Divide each exponent by $\Large 4$ : $\Large a^{\tfrac{8}{4}} b^{\tfrac{12}{4}} = a^2 b^3$ .

Practice playmedium

An estimate of escape speed, in kilometers per second, from a small asteroid can be found by multiplying the asteroid's radius, in kilometers, by $8$ and then taking the square root of the product. According to this method, what is the estimated escape speed, in kilometers per second, from an asteroid with a radius of $112$ kilometers?

The product is $112 \cdot 8 = 896$ . Factor $896 = 64 \cdot 14$ , where $64$ is the largest perfect-square factor. So $\sqrt{896} = \sqrt{64 \cdot 14} = 8\sqrt{14}$ , and $14 = 2 \cdot 7$ is square-free.