# Lesson 5

### Problem 1

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

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

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

### Problem 2

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

### Problem 3

The equation $$x^2=25$$ has two solutions. This is because both $$5 \boldcdot 5 = 25$$, and also $$\text-5 \boldcdot \text-5 = 25$$. So, 5 is a solution, and also -5 is a solution.

Select all the equations that have a solution of -4:

A:

$$10+x=6$$

B:

$$10-x=6$$

C:

$$\text-3x=\text-12$$

D:

$$\text-3x=12$$

E:

$$8=x^2$$

F:

$$x^2=16$$

### Problem 4

Find all the solutions to each equation.

1. $$x^2=81$$
2. $$x^2=100$$
3. $$\sqrt{x}=12$$

### Problem 5

Select all the irrational numbers in the list. $$\displaystyle \frac23, \frac {\text{-}123}{45}, \sqrt{14}, \sqrt{64}, \sqrt\frac91, \text-\sqrt{99}, \text-\sqrt{100}$$

### Solution

(From Unit 8, Lesson 3.)

### Problem 6

Each grid square represents 1 square unit. What is the exact side length of the shaded square?

### Solution

(From Unit 8, Lesson 2.)

### Problem 7

For each pair of numbers, which of the two numbers is larger? Estimate how many times larger.

1. $$0.37 \boldcdot 10^6$$ and $$700 \boldcdot 10^4$$
2. $$4.87 \boldcdot 10^4$$ and $$15 \boldcdot 10^5$$
3. $$500,000$$ and $$2.3 \boldcdot 10^8$$

### Solution

(From Unit 7, Lesson 10.)

### Problem 8

The scatter plot shows the heights (in inches) and three-point percentages for different basketball players last season.