1. Pythagorean Relationship
Square Roots
Pythagorean Relationship
Square Roots & “Who Wants to be a Millionaire!

2. “Minds On” Activity
2 sets of cards are posted on the board. One set represents square roots (perfect squares) and the other represents numbers squared.
Pairs are to point out and
match the equivalent square
roots and numbers squared.

3. A Couple Definitions
Square Root – A factor that multiplies by itself to give that number. The symbol is √ .
Perfect Square – A number whose square root is a whole number.
√4 = 2, √25 = 5
Non-Perfect Square - A number whose square root is not a whole number .
√28 = 5.29, √35 = 5.92

4. Explore Time ... Estimating Square Roots
Work with a partner. You will receive a copy of a number line.
With the number line, place each square root on the number line to show its approximate value. Yes, some are non-perfect squares.
Write down the strategies you used to estimate the square roots below your number line.
Square Roots √5
√18
√16 √2
√24 √9

5. Estimating Non-Perfect Squares
Estimate √86, to one decimal place.
I can use a number line to help me with non-perfect squares, like √86.
Think of the perfect squares closest to √86.
81 and 100 are the two perfect squares closest to 86.
I know that 9² = 81 and 10² = So √86 is between 9 and 10.
Now I decide which perfect square is 86 closest to.
86 is about one quarter of the way between 81 and 100
An estimate for √86 is 9.3.
You can use a calculator to find the approximate square root:
Type “86” and “√”
= 9.27
√86
√81
√100 8 9 10 11

6. Practice Questions Give the value of each square root.
Using a number line, to estimate the value of each square root.
A square garden has an area of 138m².
What are the approximate dimensions of the garden?
About how much fencing would be needed to go around the garden?
a) √64 =
b) √2500 =
c) √0.49 =
a) √50 =
b) √23 =
c) √30 =