Test Your Understanding: Estimating Non-Perfect Square Roots

📚 Quick Study Guide

• 💡 Non-perfect squares are numbers whose square roots are not whole numbers (e.g., $\sqrt{2}$, $\sqrt{10}$).
• 🔍 To estimate $\sqrt{x}$, find the nearest perfect squares $a^2$ and $b^2$ such that $a^2 < x < b^2$.
• 📝 Therefore, $a < \sqrt{x} < b$.
• ➗ Estimate $\sqrt{x}$ by determining if $x$ is closer to $a^2$ or $b^2$. If $x$ is closer to $a^2$, then $\sqrt{x}$ is closer to $a$; if closer to $b^2$, then $\sqrt{x}$ is closer to $b$.
• ➕ Refine the estimate by using decimals. For example, if you think $\sqrt{x}$ is about $a.5$, square $a.5$ and see how close it is to $x$. Adjust accordingly.

Practice Quiz

1. Which of the following is the best estimate for $\sqrt{17}$?

   1. 3
   2. 4
   3. 5
   4. 6

2. Estimate $\sqrt{35}$ to the nearest whole number.

   1. 4
   2. 5
   3. 6
   4. 7

3. Which value is closest to $\sqrt{68}$?

   1. 7
   2. 8
   3. 9
   4. 10

4. Estimate $\sqrt{120}$ to the nearest tenth.

   1. 10.4
   2. 10.9
   3. 11.0
   4. 11.4

5. What is the estimated value of $\sqrt{8}$?

   1. 1
   2. 2
   3. 3
   4. 4

6. Estimate $\sqrt{50}$ to the nearest tenth.

   1. 6.9
   2. 7.0
   3. 7.1
   4. 7.2

7. Which of the following gives the best estimate for $\sqrt{90}$?

   1. 8.9
   2. 9.2
   3. 9.5
   4. 9.8