Lesson 05: Reasoning About Square Roots | Unit 8: Pythagorean Theorem and Irrational Numbers

Open Ended

Explain how you know that $$\sqrt{37}$$ is a little more than 6.

Open Ended

Explain how you know that $$\sqrt{95}$$ is a little less than 10.

Open Ended

Explain how you know that $$\sqrt{30}$$ is between 5 and 6.

Draw

Plot each number on the number line: $$6, \sqrt{83}, \sqrt{40}, \sqrt{64}, 7.5$$

Multiple Select

The equation $$x^2=25$$ has _two_ solutions. This is because both $$5 \cdot 5 = 25$$ , and also $$-5 \cdot -5 = 25$$ . So 5 is a solution, and $$-5$$ is also a solution. Select **all** the equations that have a solution of $$-4$$ :

• $$-3x=-12$$

• $$10+x=6$$

• $$x^2=16$$

• $$-3x=12$$

• $$10-x=6$$

Multiple Choice

Each number is between which two consecutive integers? 1. $$\sqrt{10}$$

• 4 and 5
• 2 and 3
• 1 and 2
• 3 and 4

Multiple Choice

Each number is between which two consecutive integers? 2. $$\sqrt{54}$$

• 7 and 8
• 5 and 6
• 8 and 9
• 6 and 7

Multiple Choice

Each number is between which two consecutive integers? 3. $$\sqrt{18}$$

• 5 and 6
• 4 and 5
• 2 and 3
• 3 and 4

Multiple Choice

Each number is between which two consecutive integers? 4. $$\sqrt{99}$$

• 9 and 10
• 7 and 8
• 10 and 11
• 8 and 9

Multiple Choice

Each number is between which two consecutive integers? 5. $$\sqrt{41}$$

• 4 and 5
• 6 and 7
• 5 and 6
• 7 and 8