Math - 2018-19
A.3 - Roots of Expressions
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.
- 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 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.
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
· A.3a1 Express the square root of a whole number in simplest form.
the principal square root of a monomial algebraic expression in simplest form
where variables are assumed to have positive values.
· A.3b1 Express the cube root of an integer in simplest form.
· A.3c1 Simplify a numerical expression containing square or cube roots.
· A.3c2 Add, subtract, and multiply two monomial radical expressions limited to a numerical radicand.