1416 Words6 Pages

Radicals
Tips
1. Make sure that one of the two factors of the radicand (expression under the radical) is the largest perfect square: Example: Simplify 72 Correct 72 = 36 ∙ 2 = 62 Incorrect 72 = 9 ∙ 8 = 38
2. To be able to add or subtract radicals, the radicands must be the same. Example 1: Add 32 + 52 Answer: Since radicands are the same, (3 + 5)2 = 82 Example 2: Subtract 73 - 3 Answer: (7 – 1)3 = 63 Example 3: 318 - 52 (Must simplify first) 39 2 - 52 3 ∙ 3 ∙ 2 - 52 92 - 520 Answer: 42*…show more content…*

To multiply and divide radicals, perform the indicated operation on the radicands and then simplify: (You do not need radicand to be the same in order to multiply or divide) Example 1: (85) (42) = (8)(4) 5 2 = 3210 Example 2: (105) ÷ (25)= (10 ÷ 2) (5 ÷ 5) = 5 (1) = 5 Example 3: (320 ) (32) sometimes it is easier to simplify first (64 ∙ 5) (16 ∙ 2 (85) (42) Answer = 3210 Example 4: (6500) ÷ 220 ← Rewrite as a fraction and divide =*…show more content…*

A 40 foot long wire stretches from the top of a vertical pole to a stake in the ground 18 feet from the foot of the pole. Find to the nearest degree, the measure of the acute angle that the wire makes with the ground. 6. From the top of a 120 foot lighthouse, the angle of depression of a boat out at sea is 26°. Find to the nearest foot, the distance from the boat to the foot of the lighthouse. (Hint: the angle of depression is the angle formed by the horizontal and the light of sight from the lighthouse down to the boat) Factoring - Follow these steps for factoring 1. Look for GCF (Greatest Common Factor) which is the largest number and variable that each term has in common. Example 1 Factor: 12x5 + 16x2 (Find GCF, which is 4x2, put that out Solution: 4x2(3x3+ 4) front. Then divide each term by GCF to determine what is left inside the parentheses.) Example 2: 18x2y3z5 - 24x5y2z + 30x3y4z2 Solution: 6x2y2z(3yz4 - 4x3 + 5xy2z) 2. Look to see if it is a difference between two perfect squares.(need 4

To multiply and divide radicals, perform the indicated operation on the radicands and then simplify: (You do not need radicand to be the same in order to multiply or divide) Example 1: (85) (42) = (8)(4) 5 2 = 3210 Example 2: (105) ÷ (25)= (10 ÷ 2) (5 ÷ 5) = 5 (1) = 5 Example 3: (320 ) (32) sometimes it is easier to simplify first (64 ∙ 5) (16 ∙ 2 (85) (42) Answer = 3210 Example 4: (6500) ÷ 220 ← Rewrite as a fraction and divide =

A 40 foot long wire stretches from the top of a vertical pole to a stake in the ground 18 feet from the foot of the pole. Find to the nearest degree, the measure of the acute angle that the wire makes with the ground. 6. From the top of a 120 foot lighthouse, the angle of depression of a boat out at sea is 26°. Find to the nearest foot, the distance from the boat to the foot of the lighthouse. (Hint: the angle of depression is the angle formed by the horizontal and the light of sight from the lighthouse down to the boat) Factoring - Follow these steps for factoring 1. Look for GCF (Greatest Common Factor) which is the largest number and variable that each term has in common. Example 1 Factor: 12x5 + 16x2 (Find GCF, which is 4x2, put that out Solution: 4x2(3x3+ 4) front. Then divide each term by GCF to determine what is left inside the parentheses.) Example 2: 18x2y3z5 - 24x5y2z + 30x3y4z2 Solution: 6x2y2z(3yz4 - 4x3 + 5xy2z) 2. Look to see if it is a difference between two perfect squares.(need 4

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