#### Math - 2017-18

# A.3 and *A.3 - Roots of Expressions

**A.3 ** The student will
**express **the square roots and cube roots of whole numbers and the square root of
a monomial algebraic expression in simplest radical form.

A.3The student willsimplifya) square roots of whole numbers and monomial algebraic expressions;

b) cube roots of integers;

c) numerical expressions containing square or cube roots.

**Bloom's Level:** Understand

*Adopted: 2009*

### BIG IDEAS

- I can calculate area or volume, determine growth or decay,
and figure out the impact of force. I
can determine national debt and world population, program a computer game,
figure electrical voltage, and track the spread of viruses.

- I will understand that square and square root as well as
cube and cube root are inverse operations and that non-perfect squares and
non-perfect cubes are irrational.

### UNDERSTANDING THE STANDARD

- A square root in simplest form is one in which the radicand (argument) has no perfect square factors other than one.
- A cube root in simplest form is one in which the argument has no perfect cube factors other than one.
- The cube root of a perfect cube is an integer.
- The cube root of a nonperfect cube lies between two consecutive integers.
- The inverse of cubing a number is determining the cube root.
- In the real number system, the argument of a square root must be nonnegative while the argument of a cube root may be any real number.

2016 VDOE Curriculum Framework - AI.3 Understanding

· A radical expression in Algebra I contains the square root symbol () or the cube root symbol ().

·
A square
root of a number *a* is a number *y* such that *y*^{2 }= *a*.

·
A cube root
of a number *b* is a number *y* such that *y*^{3 }= *b*.

· A square root in simplest form is one in which the radicand has no perfect square factors other than one.

· The inverse of squaring a number is determining the square root.

· Any non-negative number other than a perfect square has a principal square root that lies between two consecutive whole numbers.

· A cube root in simplest form is one in which the radicand has no perfect cube factors other than one.

· The cube root of a perfect cube is an integer.

· The cube root of a nonperfect cube lies between two consecutive integers.

· The inverse of cubing a number is determining the cube root.### ESSENTIALS

**The student will use
problem solving, mathematical communication, mathematical reasoning,
connections, and representations to**

·
A.3a_{1 }**Express**
the square root of a whole number in simplest form.

A.3_{3} **Express**
the principal square root of a monomial algebraic expression in simplest form
where variables are assumed to have positive values.

·
A.3a_{2 }**Express**
the principal square root of a monomial algebraic expression in simplest form
where variables are assumed to have positive values.

·
A.3b_{1 }**Express**
the cube root of an integer in simplest form.

·
A.3c_{1 }**Simplify**
a numerical expression containing square or cube roots.

·
A.3c_{2 }**Add**,
**subtract**, and **multiply** two monomial radical expressions limited to a numerical
radicand.

### KEY VOCABULARY

*Updated: Oct 27, 2017*