# 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.3  The student will simplify

a)  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

### 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.

·  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 y2 = a.

·  A cube root of a number b is a number y such that y3 = 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.3aExpress the square root of a whole number in simplest form.

A.33  Express the principal square root of a monomial algebraic expression in simplest form where variables are assumed to have positive values.

·  A.3aExpress the principal square root of a monomial algebraic expression in simplest form where variables are assumed to have positive values.

·  A.3bExpress the cube root of an integer in simplest form.

·  A.3cSimplify a numerical expression containing square or cube roots.