Name ______________ Hour ___
Date __________________
Notes for M3S1E1 p. 165-167 #3-10
In The Mystery of Blacktail Canyon, archaeologist Dr. B. B. Ashilaka and his
daughter, Nageela, are studying ancient ruins. Their work involves finding the
dimensions of archaeological sites.
3. Discussion – The sketch shows a room at a site. See math book page
165.
a. What is the approximate shape of the room? ____________
b. Estimate the length of one side of the room. _________ How did
you make your estimate? _______________________________
c. Let s = the length of one side of the room. Write an equation
relating the area A of the room to s. _A =________________
* The area of a square can be found by multiplying the length of
one of the sides by itself, or by squaring the length of a side.
The equation A=s2 can be used to find the length of a side of a
square with a given area. See example on page 166.
4. In the Example, the number 5 is a solution of the equation s2 = 25 and is
called a square root of 25. What is another square root of 25?
_______
*If A=s2, then s is a square root of A. Since 4 2 = 16 and
(-4) = 16, both 4 and -4 are square roots of 16. The
positive solution of s 2 = 16 is called the principal square
root of 16 and is indicated by 16 .
16 = 4 The principal square root of 16 is 4.
!
! The same symbol with a minus sign, - 16 , indicates the
negative square root.
- 16 = -4 The negative !
square root of 16 is -4.
!
5. Use mental math to find each value.
a.
81
c.
b.
49
d. - 9
e. - 64
1
f.
- 144
*!
The numbers 1, 4, 9, 16, and!25 are perfect squares. A perfect
!
square is a number whose principal square root is a whole number.
!
!
!
*See examples of perfect squares on page 166.
6. List the next five perfect squares after 25.
•
_____
•
_____
•
_____
•
_____
•
_____
Now list some numbers that are not perfect squares. ____ ____ ____
*Estimating Square Roots – In Question 3 you estimated
need to estimate many square roots.
7. Calculator Use the
key to estimate
39 . You
39 . Compare
this estimate
!
with you estimate from Question 3. _______________
8. Try This as a! Class
!
a. Follow these steps to make a table.
1.
List the first 25 consecutive whole numbers in the
first column
2.
Find and record the principal square root of each
perfect square
3.
Use a calculator to estimate the principal square
roots of the other numbers.
b. Look at the whole numbers between 4 and 9. Compare their
square roots with
4 and
9 . ___________________________
c. Make some predictions about the square roots of the whole
numbers !
between !25 and 36. Check your predictions.
_____________________________________________________
9. Answer the following questions.
a. Since 45 is not a perfect square, its principal square root is not a
whole number. Is
b. Estimate
45 closer to 6 or 7? _________
45 to the nearest tenth. Do not use your calculator. ___
c. Square your
! estimate in part (b) to check for accuracy. _______
d. Use
! your result in part (c) to improve your estimate. _______
e. Use the
key on your calculator to find
45 to the nearest
thousandth. __________
f. !When can you use mental math instead
of your calculator to
!
estimate square roots? ______________________________
10. √Checkpoint – Use mental math to estimate each square root.
Then use a calculator to find each square root to the nearest tenth.
Question
a.
55
!
b.
37
!
c.
62
!
d.
103
!
Mental Math Answer
Calculator Answer