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Module 13

Simplify: √5 · √4y = Answer: √20y To solve this problem we use the product rule. Product Rule: if n√a are real numbers n√b then n√a·n√b = n√ab
Simplify: √21/25 = Answer: √21/√25 For this problem we use the quotient rule. Quotient Rule: if if n√a are real numbers n√b and n√b ≠ 0 then n√a/b = n√a / n√b
Simplify: √30/√5 = Answer: √6 In solving this problem we use the quotient rule. These are the steps used to solve: 1.Place both numbers under the square root symbols √30/5 2. Then divide √30/5 which equals √6
Find the distance between the two coordinates: (5,2) and (9,6) Answer: 4√2 We use the distance formula: √(x2-x1)²+(y2-y1)² Insert coordinates: √(9-5)²+(6-2)² Solve: √(9-5)²+(6-2)² = √(4)²+(4)² Simplify: √(4)²+(4)² = √32 Simplify: √32 = 4√2
Find the mid point of the two coordinates: (6,2) and (12,5) Answer: (9,7/2) Here we use the mid point formula: ((x1+x2)/2 , (y1+y2)/2) Insert coordinates: ((6+12)/2 , (2+5)/2) Solve: ((6+12)/2 , (2+5)/2) = ((18)/2 , (7)/2) Simplify: ((18)/2 , (7)/2) = (9,7/2)
Add the radicals: 2√50 + 5√32 = Answer:34√2 You can add or subtract like radicals. Like radicals are where the indexes and the radicands are the same. Simplify: 2√50 + 5√32 = 2√25·√2 + 5√16·√2 Simplify:2√25·√2 + 5√16·√2= 14√2 + 20√2 Now you can add like radicands: 14√2 + 20√2 = 34√
Subtract the radicals: 5∛24-∛81 =? Answer: 7∛3 You can add or subtract like radicals. Like radicals are where the indexes and the radicands are the same. Simplify: 5∛24-∛81 = 5∛8·∛3-∛27·∛3 Solve: 5∛8·∛3-∛27·∛3 = 10∛3-3∛3 Subtract: 10∛3-3∛3 = 7∛3
Multiply the radicals: (3√6+√7)(4√5-2√6)= Answer:12√30-36+4√35-2√42 To solve we are going to either the distributive property or the FOIL method. FOIL: (3√6+√7)(4√5-2√6) Multiply: 12√6·√5-6√6·√6+4√5·√7-2√6·√7 Simplify:12√30-6·6+4√-2√42 Answer: 12√30-36+4√35-2√42 You can't simplify anymore.
What is the distance formula? The distance formula is √(x2-x1)²+(y2-y1)²
What is the mid point formula? The mid point formula is ((x1+x2)/2 , (y1+y2)/2)
Created by: byers.nathan