Exponents and Square Roots Pythagorean Theorem

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Pythagorean Theorem Introduction

Objective: Find the missing side in right triangles using the Pythagorean Theorem.

Multiple Choice

3⁵ means....?

• 3 × 3 × 3 × 3 × 3

• 5 × 5 × 5

• 3 × 5

REVIEW Understanding Exponents

1² (means 1×1) = 1

2² (means 2×2)= 4

3² (means 3×3)= 9

4² (means 4×4)= 16

5² (means 5×5)= 25

6² (means 6×6)= 36

7² (means 7×7)= 49

8² (means 8×8)= 64

9² (means 9×9)= 81

Math Response

3³ = ?

Type answer here

Correct Answer: 27

Deg^°

Rad

Numbers in blue are PERFECT SQUARES

1² = 1

2² = 4

3² = 9

4² = 16

5² = 25

6² = 36

7² = 49

8² = 64

9² = 81

PERFECT SQUARES are numbers that when you take the square root the answer is a number (not a decimal)

√4 = 2

√9 = 3

√16 = 4

√25 = 5

√36 = 6

√49 = 7

...and so on

Math Response

$$\sqrt{81}=??$$  

Type answer here

Correct Answer: 9

Deg^°

Rad

NON-PERFECT SQUARES are numbers that when you take the square root the answer is a decimal

√10 = 3.16227766....(this keeps going forever)

√34 = 5.820951895...

In this situation, we are going to round to the nearest tenth.

(next slide)

ROUNDING to the nearest tenth

√10 = 3.16227766....

(look at the number to the right)

√10 = 3.16227766....

(below 5 - number stays the same)

(5 or above - number goes up one)

6 is above 5 - the 1 becomes a 2

√10 ≈ 3.2

ROUNDING to the nearest tenth

√34 = 5.820951895...

(look at the number to the right)

√34 = 5.820951895...

(below 5 - number stays the same)

(5 or above - number goes up one)

2 is below 5 - the 8 stay an 8

√34 ≈ 5.8

Math Response

Round √166 to the nearest tenth

Type answer here

Correct Answer: 12.9

Deg^°

Rad

Solving Equations with Square Roots

​Solve: x² = 25

​Solve: x² = 26

Math Response

Solve: x² = 121 (if necessary round the answer to the nearest tenth)

Type answer here

Correct Answer: 11

Deg^°

Rad

Math Response

Solve: x² = 39 (if necessary round the answer to the nearest tenth)

Type answer here

Correct Answer: 6.2

Deg^°

Rad

Math Response

Solve: x² = 98 (if necessary round the answer to the nearest tenth)

Type answer here

Correct Answer: 9.9

Deg^°

Rad

Open Ended

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