Presentation on theme: "Drill #37 Factor the following polynomials Simplify."— Presentation transcript:
1 Drill #37 Factor the following polynomials Simplify. Find the value of r:
2 Drill #38Factor the following polynomialsSimplify.
3 Drill #60 Factor the following polynomial Evaluate the following roots:
4 7-4 Nth RootsObjective: To simplify radicals having various indices, and to use a calculator to estimate the roots of numbers.
5 Square Roots What power is a square root? A square is the inverse of a square root…
6 Square Root* Definition: For any real numbers a and b, if then a is a square root of b orWe can also write square roots using the ½ power.
7 Cube Root* Definition: For any real numbers a and b, if then a is a cube root of b orWe can also write cube roots using the 1/3 power.
8 nth Root* Definition: For any real numbers a and b, if then a is a nth root of b orWe can also write nth roots using the power.
9 How many ways can you … Multiply two numbers to get a positive #? Multiply two numbers to get a negative #?
10 Examples: Roots (of powers of 2) Even Roots: Odd Roots:
11 Principal Root*Definition: When there is more than one real root of a number (even numbered roots), the non-negative root is the principal root Principal Root Negative Root Both
12 Examples: Roots (of powers of 2) Both Principal NegativeRoots: Roots: Roots:
13 Roots of negative numbers* Even roots: Negative numbers have no even roots. (undefined)Odd Roots: Negative numbers have negative roots.
14 Examples: Roots (of powers of 2) Even Roots: Odd Roots:
15 Roots: Number and Types Even RootsOdd RootsPositive2 (one positive, one negative)1 (positive)Negative0 (undefined)1 (negative)
16 Even Roots (of variable expressions)* When evaluating even roots (n is even) use absolute values (if resulting power is odd).
17 Odd Roots (of variable expressions)* When evaluating odd roots (n is odd) do not use absolute values.
18 Evaluating Roots of Monomials To evaluate nth roots of monomials:(where c is the coefficient, and x, y and z are variable expressions)orSimplify coefficients (if possible)For variables, evaluate each variable separately
19 Evaluating Roots of Monomials* To find a root of a monomialSplit the monomial into a product of the factors, and evaluate the root of each factor.Variables: divide the power by the root Coefficients: re-write the number as a product of prime numbers with powers, then divide the powers by the root.
20 Use a calculator to find the roots* Find the following roots using a calculator (round to the 3 decimal places):