Warm-up Estimate the following to the thousandths place

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Presentation transcript:

Warm-up Estimate the following to the thousandths place. 187.6539 98.7618 721.4503 3.8537 0.0007

Intro to Radicals

What is a radical?

Radicals A radical can be a square root, cubed root, fourth root, etc! Inverse operation of exponents Just like we “undo” addition with subtraction, and “undo” multiplication with division, we “undo” exponents with radicals!

What are perfect squares

Estimating Square Roots What happens when the radicand is not a perfect square, cube, etc?

Estimating Square Roots The square root has to be in between two integers. So think about the perfect squares that are above or below the number. Example: 55 So 55 is between 49 and 64, so therefore the 55 has to be between 7 and 8.

Estimating Square Roots Example: 90 Example: 80 Example: 105

Estimating Square Roots: Application You want to sew a fringe on a square tablecloth with an area of 500 square inches. Calculate the length of each side of the tablecloth and the length of fringe you will need to the nearest inch. 500 = approximately 22 inches so you will need about 88 inches of fringe

Estimating Square Roots: Application You want to build a fence around a square garden that is 250 square feet. Calculate the length of one side of the garden and the total length of the fence. 250 = approximately 16 ft

Estimating Square Roots: Using Calculator Example: 141 Example: 154 Example: 600 Example: 800

What do we do if radicals are NOT perfect squares? SIMPLIFY THEM!

Radicals are in SIMPLEST FORM 1. No perfect square factors other than 1 are under the radical. 2. No fractions are under the radical. 3. No radicals are in the denominator.

To simplify radicals (with numbers under the radical): Create a Factor Tree- circle ALL prime numbers Write all prime factors under the radical Circle any pairs Move ONE of each pair to the front Multiply remaining numbers if necessary

Step 1: Create factor trees to find prime factors What are prime numbers? A number greater than one that only has the factors of one and itself! 2, 3, 5, 7, 11, 13, …

Factor Trees to Prime Factorization 45

Factor Trees to Prime Factorization 54

Factor Trees to Prime Factorization 98

When you have a pair, bring the number out. EX:1 Simplify. When you have a pair, bring the number out.

When you have a pair, bring the number out. EX:2 Simplify When you have a pair, bring the number out.

EX:3

EX:4 Simplify.

You try! 1. 2. 3. 4.