Estimating Square Roots of Non-Perfect Squares
About this lesson
Students recall perfect squares, then work in pairs to estimate square roots of numbers like 30 or 90 to one decimal place. They place their estimates on a class number line and check them by squaring. It takes about 15 minutes and needs only the whiteboard, scrap paper and sticky notes.
- Grade
- 8
- Subject
- Math
- Time
- 15 min
- Prep
- 3 min
Objective
Students will estimate the square root of a non-perfect square to one decimal place by locating it between two consecutive perfect squares.
Prep
3 min: draw a number line from 0 to 15 on the board and write 20, 45, 70, 90, 115, 150 and 200 beside it
Materials
- whiteboard and marker
- scrap paper
- pencils
- sticky notes
Steps
- Run a quick-fire round of perfect squares: call out a number from 1 to 15 and have the class answer with its square (for example, you say 7, they say 49).
- Model √30 on the board: it sits between 25 and 36, so the root is between 5 and 6, and because 30 is a little closer to 25, estimate about 5.4.
- Have pairs estimate the square root of each board number to one decimal place, writing the two perfect squares it falls between before giving their estimate.
- Give each pair one sticky note for one number, then ask a member of each pair to write their estimate on it and place it on the class number line.
- Check a few estimates together by squaring them on paper (5.4 × 5.4 = 29.16), and ask the class which estimate came closest and why.
Quick Check
Have each student write an estimate for √55 on scrap paper as an exit slip. Look for an answer of about 7.4 and the reasoning that 55 lies between 49 and 64.
Differentiation
Make it easier: Have students only name the two whole numbers the root falls between, without a decimal estimate.
Make it harder: Ask students to estimate to two decimal places and refine their answer by squaring and adjusting, or to estimate roots of numbers like 0.5 or 300.
Good For
- Morning warm-up
- Review
- Supply teacher
- Before lunch
