Exponents Outline for Topic 5: Square Root
Concept: Square Root
Name:
Warm Up
1. Multiply the following:
(a) 22 = (b) 32 = (c) 42 =
(d) 52 = (e) 62 = (f) 72 ==
COMPUTER COMPONENT
Instructions: Select the computer program Understanding Exponents (Neufeld)
Follow the instructions to the Main Menu.
Select Square Root from the Main Menu.
Work through all sections of this topic in order:
• Squaring Numbers
• Square Roots
• Radical Signs
• Square Roots of Negative Numbers
• Examples Questions
• Estimating Square Roots
• Estimating Square Roots on a Number Line
• Practice Questions
Additional Required Materials: Scientific calculator
As you work through the computer exercises, make your notes in the
NOTES section of this page.
When you reach the end of the section Practice Questions on the computer,
move on to the OFF COMPUTER EXERCISES below.
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Exponents Outline for Topic 5: Square Root
NOTES
Squaring Numbers
A number is squared when it is ____________________ by _____________.
Fill in the following examples of squares.
12 = 1 1 = 1
22 = ____ ____ = _______
(-2)2 = ____ ____ = _______
72 = ____ ____ = _______
(-7)2 = ____ ____ = _______
4.52 = ____ ____ = _______
(-4.5)2 = ____ ____ = _______
a2 = ____ ____ = _______
(-a)2 = ____ ____ = _______
Fill in the blanks.
(a) Every positive number has ____ square roots; one _____________________
and one _______________________________.
Example:
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Exponents Outline for Topic 5: Square Root
22 = 2 ______ = ______
(-2)2 = ( -2 ) ( ____ ) = _____
The square roots of __________ are ________ and _______ .
(b) The symbol is called a ___________________ sign.
(c) The radical sign tells you to take the______________________ square root.
What number has been squared to get the number under the square root symbol?
(a) 64
(b) 25
A number cannot be _____________________ by __________________ to give a
__________________ product.
Example: -4 2 2 = 4
-2 -2 = 4
The product is always a __________________ number.
We ______________________ take the square root of a _______________________ number.
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Exponents Outline for Topic 5: Square Root
Remember:
Operations ______________ the _________________ sign are done _________.
Example:
4 + 10 =
________
= ________
A square root can be written as a __________ of two radicals.
Example:
(a) 6 = 2 3
= ___ ___
(b) 9 = 3 3
---
= ( )
___
When estimating square roots.
First, find an easier square root that is close, but a little _____________than it.
Then find an easier square root that is just a little ____________ than it.
Example:
(a) 28 is ____________ and
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Exponents Outline for Topic 5: Square Root
OFF COMPUTER EXERCISES
1. Find the square roots of each number.
(a) 81 (b) 64
(c) 1 (d) 0
(e) 100 (f) 144
(g) 9 (h) 225
2. Which square roots are the following between?
(a) 72
(b) 38
(c) 109
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Exponents Outline for Topic 5: Square Root
3. Fill in the missing numbers on the radical clock face:
4. Evaluate.
(b) -
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Exponents Outline for Topic 5: Square Root
(c)
(d) -
(e) +
(g)
(h)
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Exponents Outline for Topic 5: Square Root
(i)
(j)
(k)
(l) 4 +
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Exponents Outline for Topic 5: Square Root
5. Evaluate each expression if x = 3, y = -4 and z = -7.
(a) -
(b)
(c)
(d)
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Exponents Outline for Topic 5: Square Root
6. Answer the following and show all your steps.
(a) If the area of a square is 289 square mm, calculate the dimensions.
(b) If the area of a square is 0.0081 square cm, calculate the dimensions.
(c) A rectangle has dimensions of 4 cm by 16 cm and is equal to a second figure
which is a square. Find the dimensions of the square.
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Exponents Outline for Topic 5: Square Root
Challenge
6. Calculate the square root of (43 + 43 + 43 + 43).
7. Find a number x to make this statement true:
4 + ( x ÷ 42) – 2 32 = 18
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