Lesson 4

Plot each number on the \(x\)-axis: \(\sqrt{16},\text{ } \sqrt{35},\text{ } \sqrt{66}\). Consider using the grid to help.

Use the fact that \(\sqrt{7}\) is a solution to the equation \(x^2 = 7\) to find a decimal approximation of \(\sqrt{7}\) whose square is between 6.9 and 7.1.

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.

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

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:

\(10+x=6\)

\(10-x=6\)

\(\text-3x=\text-12\)

\(\text-3x=12\)

\(8=x^2\)

\(x^2=16\)

Find all the solutions to each equation.

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

The points \((12, 23)\) and \((14, 45)\) lie on a line. What is the slope of the line?