Warm-Up

Name___________ Date___________Expand first, then evaluate the power.

1.72 =2.(-4)2 =3.32 =4.-62 =5.122 =6.(-10)2 =

Square Roots

How do you find the length of each side of a human chess board?

Wait a minute!

Did you say HUMAN

chess board?

Yup! Human

chess board!

How do you find the length of each side of a human chess board?

Before we answer the math question…let’s find out about the human chess board…

Living Chess Game in Marostica, Italy

How do you find the length of each side of a living chess board?

Now back to our question…If you know the area of the human chess

board is 324 square meters, what is the length of each side of the human chess board? How would you calculate it?

You would find the square root of 324.√324In other words…what times what =324

A square root of a number n is a number m such that m 2 = n.

Every positive number has two square roots. The square root of 25 is 5 because 5 2 =

25.

One square root is positive and the other is negative.

The square root of 25 is also -5 because (-5)2 = 25.

Square Root

The radical sign, , represents a nonnegative square root.

The symbol , - read “negative the square root of” refers to the negative square root only.

The symbol, “plus or minus,” refers to both square roots of a positive number.

Examples

Positive square root of 100

Negative square root of 100

Positive or negative square root

of 100What is ? Zero has only one square root, itself

10100

10100

10100

0

Finally…the answer!

The human chessboard of Marostica, Italy is a square with an area of 324 square meters, so the length of each side of the chessboard is the positive square root of 324.

Answer The length of each side of the chessboard is 18 meters.

.32418 because 18324 2

Find the square roots of the number.

1. 162. 643. 1444. 2565. -496. 1

What if you don’t have a perfect square and you have to find the square root of the

number?

First…what is a perfect square?

Perfect Squares

Reals

Irrationals Rationals

Perfect Squares0149162536496481100

0 0

1 1

2 1.414

3 1.732

4 25 2.2366 2.4497 2.6468 2.828

9 3

Where do perfect squares get their name?

Perfect Squares0149162536496481100

Find the area ofthe square below.

7

A = s

A = 7 = 49 un.

2

2 2

Find the side ofthe square below.

A = 16 square units

A = s2

16 = s2

S = 4

is an irrational number and we will never know its exact value.

7

However, = = 77 7 49

Square of Square Root Property

( ) = n n2

Simplify the following:

1) 2) 3) ( 11)2 2 13 8 8

Warning for tests and quizzes!!!

If you try to use a calculator to solve theproblem below, you won’t get the right answer.

=

(2.2360679)(2.2360679) = 4.9999996

5 5 5 2.2360679

The correct method gives...

= ( ) = 5 5 5 52

What if you don’t have a perfect square and you have to find the square root of the

number?

We will approximate a square root!Approximate to the nearest integer.

1.The perfect square closest to, but less than, 51 is 49.

2.The perfect square closest to, but greater than, 51 is 64.

3.So, 51 is between 49 and 64. 4.This statement can be expressed by the

compound inequality49 51 64.

51

5. 49 51 64 Identify perfect squares closest to 51.

6. Take positive square root of each number.

7. Evaluate square root of each perfect square.

Answer: Because 51 is closer to 49 than to 64, is closer to 7 than to 8.

So, to the nearest integer,

645149

8517

51

751

Now it’s your turn!

Approximate to the nearest integer.

Follow all the steps as shown in Example 2 on page 454 in your textbook.

125

Evaluating a Radical Expression

Evaluate when a = 11 and b = 5.

Show all work.

22 ba

Homework—Quiz on Wednesday on perfect squares.

Memorize the first 20 perfect squares and their square roots. You will find a table of squares and square roots on p. 822 in your textbook.

Written homework: Do not use a calculator!Pp. 456-457 16-31 odd, 41-57 odd