We can estimate square roots in three ways: 1. To the nearest whole number by finding the square root of the nearest perfect square 2. To the nearest tenth by thinking of numbers smaller and larger than the given number 3. Using a calculator, which provides an estimate even for perfect squares if the answer is rounded The key points are that not all numbers have exact square roots, so we estimate the square roots of non-perfect squares in various ways, and using a calculator gives us an approximation when rounding the answer.

1. Estimating Square Roots Math 8
By the end of class today I will be able to:
-Estimate a square root to the nearest whole number
-Estimate a square root to the nearest tenth
-Estimate a square root using a calculator
To begin: We have three questions to see what we understand so far about square numbers. Please do the three questions and then
compare your answer with a partner. Let your teacher know when you are finished.
4

2. Can I make a square with area of 25 square units?
Can I make a square with area of 20 square units?
http://www.quia.com/mc/65631.html
http://www.mathebook.net/middleschool/virtual/sqrt.htm
Try it on a piece of graph paper.

3. Write out the numbers from 1 to 12
Beneath them write each number as a square root
Use the numbers above to estimate
smaller bigger

5. We can estimate square roots to the nearest whole number
We can also estimate roots to decimal places.
Ex: Estimate
to the nearest tenth (that's ___ decimal place)
Use a number
Line!
Use a calculator to check your answer

6. Once I estimate a square root, I can check my answer with a calculator
ex: Estimate
check your answer with a calculator. Why is it not right on?

7. Even when you calculate the square root of a number that is not a perfect square using your calculator, we are really only
estimating it. Why?
Use your calculator to find the following. Round your answer to one decimal place.

8. Summary:
Not all numbers are perfect squares.
Numbers that are not perfect squares have square roots that are not whole numbers
We can estimate square roots of these numbers three ways:
1. By finding the square root of the nearest number that is a perfect square
2. By thinking of a number smaller and larger than our number, we can estimate the root to a decimal value. We can check our work with
a calculator
3. We can use our calculator to find the square root. If we are rounding our answer, it is still only an estimate.
is the symbol for "approximately equal to"