Name:______
Algebra I
Radicals
One: To find the square roots of numbers with rational square roots
Square root: if is the square root of
Radical sign:
Radical: is the radical
Radicand: 25 is the radicand
Product Property of Square Roots:
Quotient Property of Square Roots:
Examples: Find the indicated square roots.
Two: To approximate irrational roots
Irrational number: a real number that cannot be written
in the form , where and are
integers and
** can’t be written as a fraction **
Examples: Estimate the square root AND give the two whole numbers each square root falls between. Show your estimation work!
- _____ < < _____ estimate: ______integers: ______
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Three: To write rational numbers in decimal or fraction form
Terminating decimals: a number that has a finite number of decimal places
Repeating decimals: repeating digits
Examples: Express each rational number as a terminating or repeating decimal. Show your work!
Write each decimal in the form , where and are integers, . Simply!
Bonus: To find Greatest Common Factor and Least Common Multiple
Prime Factorization: a composite number expressed as a
product of prime factors (in order from least to
greatest and expressed with exponents)
Greatest Common Factor: the greatest number that is a
factor of two or more numbers
Least Common Multiple: the least of the nonzero common
multiplies of two or more numbers
Examples: Directions: Find the Greatest Common Factor (GCF) AND the Least Common Multpile (LCM). (Show your ladder method work.)
Four: To simply square roots
Simplest form:
- the radicand, no square other than one
- no denominator contains a radical
Examples: Directions: Simplify and assume all variables are greater than or equal to zero. Show all ladder method work.
Five: To simplify sums and differences of radicals
One rule: simplify first, then add/subtract
Examples: Directions: Simplify THEN Perform the indicated operations. Assume that all variables represent nonnegative real numbers. (Show your ladder method work when simplifying.)
7.Six: To simplify products of radicals
One rule: multiply, then simplify
FOIL method: First, Outer, Inner, Last
Examples: Directions: Multiply THEN Simplify. (Show your ladder method work when simplifying.)
Seven: To simplify quotients of radicals
Rationalizing the denominator: changing a fraction with an irrational denominator into a fraction with a rational denominator (simplify first)
Examples: Directions: Rationalize the denominator AND Simplify. Show all work.
Nine: To use the Pythagorean theorem to find the length of a leg or the length of the hypotenuse of a right triangle
Hypotenuse: in a right triangle, the side opposite the right angle is the longest side
Leg: the other two sides of a right triangle
Picture:
Pythagorean theorem:
In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs.
Examples: Directions: Use the Pythagorean Theorem to find the missing lengths. Show the formula, substitution, and your steps, one line at a time.
Directions: The lengths of three sides of a triangle are given. Is it a right triangle? Show the formula, substitution, and your steps, one line at a time.