# Concept Square Root

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```					                                                            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)
Select Square Root from the Main Menu.

Work through all sections of this topic in order:
• Squaring Numbers
• Square Roots
• Square Roots of Negative Numbers
• Examples Questions
• Estimating Square Roots
• Estimating Square Roots on a Number Line
• Practice Questions

As you work through the computer exercises, make your notes in the

When you reach the end of the section Practice Questions on the computer,
move on to the OFF COMPUTER EXERCISES below.

Neufeld Learning Systems Inc. 2008
www.neufeldmath.com                                                          1
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:

Neufeld Learning Systems Inc. 2008
www.neufeldmath.com                                                            2
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.

Neufeld Learning Systems Inc. 2008
www.neufeldmath.com                                                              3
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

Neufeld Learning Systems Inc. 2008
www.neufeldmath.com                                                                    4
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

Neufeld Learning Systems Inc. 2008
www.neufeldmath.com                                                           5
Exponents Outline for Topic 5: Square Root

3. Fill in the missing numbers on the radical clock face:

4. Evaluate.

(b)              -

Neufeld Learning Systems Inc. 2008
www.neufeldmath.com                                                       6
Exponents Outline for Topic 5: Square Root

(c)

(d)                 -

(e)             +

(g)

(h)

Neufeld Learning Systems Inc. 2008
www.neufeldmath.com                                                 7
Exponents Outline for Topic 5: Square Root

(i)

(j)

(k)

(l) 4 +

Neufeld Learning Systems Inc. 2008
www.neufeldmath.com                                                 8
Exponents Outline for Topic 5: Square Root

5. Evaluate each expression if        x = 3,         y = -4 and     z = -7.

(a)       -

(b)

(c)

(d)

Neufeld Learning Systems Inc. 2008
www.neufeldmath.com                                                              9
Exponents Outline for Topic 5: Square Root

(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.

Neufeld Learning Systems Inc. 2008
www.neufeldmath.com                                                          10
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

Neufeld Learning Systems Inc. 2008
www.neufeldmath.com                                                       11

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