Lesson 5: Practice Problems

Problem 1

Explain how you know that $\sqrt{37}$ is a little more than $6$ .
Explain how you know that $\sqrt{95}$ is a little less than $10$ .
Explain how you know that $\sqrt{30}$ is between $5$ and $6$ .

Problem 2

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

A number line with 6 evenly spaced tick marks and the integers 5 through 10 are indicated.

Problem 3

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 also -5 is a solution.

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

$10 + x = 6$
$10 - x = 6$
$- 3 x = - 12$
$- 3 x = 12$
$8 = x^{2}$
$x^{2} = 16$

Problem 4

Find all the solutions to each equation.

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

Problem 5 From Unit 8 Lesson 3

Select all the irrational numbers.

$\frac{2}{3}$
$\frac{- 123}{45}$
$\sqrt{14}$
$\sqrt{64}$
$\sqrt{\frac{9}{1}}$
$- \sqrt{99}$
$- \sqrt{100}$

Problem 6 From Unit 8 Lesson 2

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

A square, not aligned to the horizontal or vertical gridlines, is on a square grid. The square is drawn such that the first vertex of the square is on the left side. The second vertex is 2 grid squares up and 3 grid squares right from the first vertex. The third vertex is 3 grid squares down and 2 grid squares right from the second vertex. The fourth vertex is 2 grid squares down and 3 grid squares left from the third vertex. The first vertex is 3 grid squares up and 2 grid squares left from the fourth vertex.

Problem 7 From Unit 7 Lesson 10

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

$0.37 \cdot 10^{6}$ and $700 \cdot 10^{4}$
$4.87 \cdot 10^{4}$ and $15 \cdot 10^{5}$
$500, 000$ and $2.3 \cdot 10^{8}$

Problem 8 From Unit 6 Lesson 4

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

Circle any data points that appear to be outliers.
Compare any outliers to the values predicted by the model.