and

Square

sSquare

s

Square Roots

Square Roots

If a square measures 4 inches on each side, how would you find its area?

4 inches4

inch

es 4

inch

es

4 inches

We will:• Understand the meaning of squaring a

number and finding the square root of a number

• Find squares of numbers• Raise a whole number to a whole

number power• Find square roots of perfect squares• Find approximate square roots of non-

perfect squares

Why do we need to be able to square and find the root of a number?

• Squares and square roots are used in the Pythagorean Theorem

• Squares and square roots are used frequently in Algebra

Remember how to calculate the area?

4 inches A = l •

w A = 4 in. • 4 in. 4

in

ches

A = 16 in.2

A square must have the same length and

width. 4 inches

A = l • w A = 4 in. • 4 in.

4

inch

es

To square a number means to multiply it by

itself.

5 squared means 5 x 5

Take the number 5

And square it!

There is a shorter way to write 5 x 5.

Say:“5 squared” or

“5 to the 2nd power”.

These are the parts.

This is the base

This is the exponent

What are exponents?

Remember multiplication is repeated addition:

Exponents are repeated multiplication:

4 x 5 = 4 + 4 + 4 + 4 + 4

45 = 4 x 4 x 4 x 4 x 4

What do the parts mean?

Tells you what to multiply...

Tells you how many...

= 5 x5 x 5 x 5

Evaluate it!

= 5 x5 x 5 x 5

B. 625A. 20

This is another formula for finding the area of a

square.

sA = s

2

s is the side length

Evaluate it!

B. 49A. 14

Radicals (also called roots) are directly related to exponents.

The symbol used to indicate a root is the radical symbol -

Every radical expression has three parts…

Index

Radicand

Radical

2 49

but is normally written as .

The square root of 49 could be written as …2 49

49

What does square root mean?

The square root of a number is another number which when multiplied by itself gives back the original number.

What is a square root?

the measure of the side of the square

16 = 4

?

What is the square root of 36?

36 =6

49777 2

Example:

because

Also

because

749

749 49777 2

These numbers are called perfect squares

If a number is a perfect square, then you can find its exact square root.

A perfect square is simply a number that can be written as the square of another number.

What are the first 10 whole numbers that are perfect squares?

1, 4, 9, 16, 25, 36, 49, 64, 81, 100

2222222222 10,9,8,7,6,5,4,3,2,1

Not all numbers have an exact square root as in the previous examples.

What if you are asked to find the square root of a

non-perfect square?

Find the two closest perfect squares.

16 = 4

The square root of 15 must be between 3 and 4, closer to 4.

9 = 3

20 would be between which two whole

numbers?

25 = 5

16 = 4

20Between 4 and 5

Use the next process to find a close approximation for the square root of 10.

Is 10 a perfect square?

Can you make a square out of these ten tiles?

Is 10 a perfect square?

Can you make a square out of these ten tiles?

Can we approximate (get close to) the square root of

10?

You have to make a square out of the ten tiles

What is the length of each side?

close !

Can we approximate (get close to) the square root of

10?

16

Is 3 a good approximation of 10

?

163

= 3.1666666666666... 3.1622776601683...10

Most standardized tests only ask for

approximations like this:

153 is between which of the following consecutive whole numbers?

A. 15 and 16

B. 9 and 10

C. 12 and 13

D. 76 and 77

1. A student earned a grade of 80% on a math test that had 20 problems. How many problems on this test did the student answer correctly?

2. A metal bar weighs 8.15 ounces. 93% of the bar is silver. How many ounces of silver are in the bar?

3. Cost of sled: $99.50 Markup: 95%Find the selling price.

4. Cost of a comic book: $3.95Markup: 20%Find the selling price.

QuizQuiz1. Evaluate 72 2.Evaluate 1443.Evaluate 33

4. 200 is between what two consecutive whole numbers?

491227

14 and 15