Download Discovering Square Root Investigation

WARM-UP:
1. a.
Find the area of the following squares. Show your work.
b.
c.
7mm
1.5 in
2. As a group come up with 3 ways to find the area of a square.
1)
2)
3)
WARM-UP:
1. a.
Find the area of the following squares. Show your work.
b.
c.
7mm
1.5 in
2. As a group come up with 3 ways to find the area of a square.
1)
2)
3)
Discovering Square Root Investigation
Part I: Exploring square root with area and side length of squares.
For 1 a-c, find the side length of each square.
1. a.
b.
c.
Area 16 m2
Area 81 cm2
2. How do you think you’d find the square root of 80?
In square 1a you can count the squares and tell that the square of area 36 has a side length of 6. You
could also think in your head, “What number times itself is 36?” The answer is that 6 • 6 is 36. The
square root is the operation that undoes the operation of squaring, so 36 is 6. 36 is read as “the
square root of 36”.
3. Find the side length of the following squares using the square root.
a.
b.
c.
Area of 1 in2
Area of 169 cm2
Area of 36 ft2
When you are finding the square root of a number within the square root sign,
, you are finding the positive
root. This is called the principal root.
4. Find the principal root of the following numbers.
a.
100
b.
49
c.
50
There is a trick with square roots when you work with negative numbers. You know that:
5 • 5 = 25 and -5 • -5 = 25. So when you find the roots of 25, the answer can be 5 and it can be -5. Every
number has 2 roots, positive and negative.
5. Find the two roots for the following perfect square numbers. (Note, you are being asked to find the roots of a
number and there is NO square root symbol present.)
a) 81
b) 121
c) 144
d) -49
6. What did you do for question 5d? What number times itself will give you -49?
a) Is -7 • -7 = -49?
You cannot find the
negative answer!
b) Is 7 • 7 = -49?
-49 because there is no real number that can be multiplied by itself to get a
7. The table below shows that a side length can be squared to find the area. We will fill in the missing blanks
in the table AS A CLASS.
Perfect Square
(area)
Twin factors
(side lengths)
Squares
Square roots
Visual
49
11, -11
0.22 = 0.04
(-0.2)2 = 0.04
225
Part II: Order of operation with square roots.
8. Since finding the square root is like undoing an exponent, square roots are evaluated at the same time as
exponents. Solve the problems below, evaluating square roots before any multiplying, dividing, adding, or
subtracting. Show all your work.
a) 3 + 4 25
c) - 1 + 4
b) 3(9 - 36)
9. What is the difference between the two expressions given for the following problems? Solve them. You
should come up with 2 different answers.
a) 9 + 25and 9 + 25
b) 4 25and25 4