11.1 Square RootsDefinition Example

Square root - a number that produces a specified quantity when multiplied by itself.

The square root of 25 is 5, since 5 x 5 = 25.

Perfect square or Square number – A number that is the square of an integer.

9 is a perfect square because 9 = 32

Radical expression – An expression involving a radical sign.

36CopyInto

Notes

So, the square root of 25 is 5.

We write it:

Finding Square RootsSquare Root – A number which, when multiplied

by itself, results in another number.

52 =

25 5

25

Perfect SquaresPerfect square – A number that is a square of a whole number.

Can be represented by arranging objects in a square.

You need to memorize the first 15 perfect squares.

Perfect SquaresLets find them…

Squared Perfect Square

Square Root

12 = 1 √1=1

22=

32 =

42 =

52 =

62 =

82 =72 =

4

9

16

25

36

6449

√4=2

√49=7

√64=8

√36=6

√25=5

√9=3

√16=4

Squared Perfect Square

Square Root

92 = 81 √81=9

102 =

112 =

122 =

132 =

142 =

152 =

100

121

144

169

196

225

√100=10

√225=15

√196=14

√169=13

√121=11

√144=16

Write this down!

Square Roots

81

169

37

Estimating Square Roots.

Since 37 is not a perfect square, we have to use another method to calculate it’s square root.

Most numbers are NOT perfect squares and their solutions are not whole numbers.

37

Find the two square roots of the number.

1) 49

2) 121

3) 3600

Evaluate the square root.

4) .

5) .

6) .

900

196

16

Find the side length of the square with the given area.

7) .

8) .

A 4m2

A 256cm2

Evaluate the expression when x=2, y=5, and z=-1

9) .

10).

16z

x 2 y 2 20

Solve the equation.

11) .

12).

3b2 75

15 d2 96