Download Part 1- Calculating Perfect SQuares When 9 is squared it equals 81

Name _______________________________________
Square Roots Activity
Part 1- Calculating Perfect SQuares
What is the value of the following:
22 = _______
32 = _______
52 = _______
Find the area of the squares:
72 = _______
5
3
Area = ________
Area = ________
Find the area of a square with side 4.
Find the area of a square with side n.
If the area of a square is 49 inches squared. What is its side length?
What number can you square to equal 81?
What number can you square to equal 121?
When 9 is squared it equals 81. So we can say 9 is the square root of 81. √
is the
square root symbol, so you would read √81 = 9 as the square root of 81 equals 9.
Write in your own words how to find √25.
Square Number also called a perfect square, is a number that can be represented
by the square of a whole number.
Complete the table.
Square Root
Process
Perfect Square
1
1●1
1
2
2●2
4
3
3●3
9
36
8
100
13
225
Part 2- Evaluating Square Roots (Using a Calculator)
Using your calculator, calculate the following. Round to the nearest thousandth if necessary.
√115
√38
√12
√169
√31
√625
√225
√72
√110
Using your calculator type in √−9. Why do you think you get an error? (Hint: What number when
multiplied by itself is –9?)
Part 3- Estimating Square Roots (Without Using a Calculator)
Not all numbers are perfect squares. For an integer that is not a perfect square, you can estimate a
square root. To estimate the value of a square root, find the two perfect squares that the number lies
between.
Example #1: Estimate the value of √6.
To do this, you need to find the two perfect squares that are directly above and below the number.
Fill in the blanks in the inequality below with the perfect square directly above and below √6:
_______ < √6 < _______
Next, take the square root and fill in the blanks with the integer directly above and below √6.
_______ < √6 < _______
Lastly, √6 is closer to __________; therefore, √6 is closer to __________.
Solution: √6 falls between ________ and ________, but closer to ________.
Example #2: Estimate the value of √34.
Use perfect squares to complete the first inequality:
_______ < √34 < _______
Use integers to complete the second inequality:
_______ < √34 < _______
Lastly, √34 is closer to __________; therefore, 34 is closer to __________.
Solution: √34 falls between ________ and ________, but closer to ________.
Let’s Practice!
1. Between which two whole numbers does √19 fall?
__________ < √19 < __________
__________ < √19 < __________
Therefore, √19 falls between ________ and ________.
2. Between which two whole numbers does √28 fall?
__________ < √28 < __________
__________ < √28 < __________
Therefore, √28 falls between ________ and ________.
3. Between which two whole numbers does √60 fall?
__________ < √60 < __________
__________ < √60 < __________
Therefore, √60 falls between ________ and ________.
4. Between which two whole numbers does √74 fall?
5. Between which two whole numbers does √95 fall?
Estimate the value of each square root, then place the value in the correct place on the number
line.
√14
√27
√45
√34
_______ < √14 < _______
_______ < √27 < _______
_______ < √45 < _______
_______ < √34 < _______
_______ < √14 < _______
_______ < √27 < _______
_______ < √45 < _______
_______ < √34 < _______