Lesson 4
Square Roots on the Number Line
Problem 1

Find the exact length of each line segment.

Estimate the length of each line segment to the nearest tenth of a unit. Explain your reasoning.
Solution
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Problem 2
Plot each number on the \(x\)axis: \(\sqrt{16},\text{ } \sqrt{35},\text{ } \sqrt{66}\). Consider using the grid to help.
Solution
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Problem 3
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.
Solution
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Problem 4

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.
Solution
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Problem 5
Plot each number on the number line: \(\displaystyle 6, \sqrt{83}, \sqrt{40}, \sqrt{64}, 7.5\)
Solution
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Problem 6
The equation \(x^2=25\) has two solutions. This is because both \(5 \boldcdot 5 = 25\), and also \(\text5 \boldcdot \text5 = 25\). So, 5 is a solution, and also 5 is a solution.
Select all the equations that have a solution of 4:
\(10+x=6\)
\(10x=6\)
\(\text3x=\text12\)
\(\text3x=12\)
\(8=x^2\)
\(x^2=16\)
Solution
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Problem 7
Find all the solutions to each equation.
 \(x^2=81\)
 \(x^2=100\)
 \(\sqrt{x}=12\)
Solution
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Problem 8
The points \((12, 23)\) and \((14, 45)\) lie on a line. What is the slope of the line?
Solution
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(From Unit 5, Lesson 4.)