HW # 48- p. 194 # 1-37 odd

Warm up

Week 14, Day Two

Simplify.

1. 52 2. 82

3. 122 4. 152

5. 202 6. x2 * y7 * x-1 * y3

HW # 48- p. 194 # 1-37 odd

Warm up

Week 14, Day Two

Simplify.

25 64

144 225

400

1. 52 2. 82

3. 122 4. 152

5. 202 6. x2 * y7 * x-1 * y3 𝑥 𝑦 10

Homework CheckPractice Worksheet 4-5

1) 11,580,000 2) 131,6003) 0.002185

4)7.5 X 107 5) 2.08 x 102

6)9.071 x 105

7) 5.6 x 101 8) 9.3 x 10-2 9) 6.0 x 10-5

10) 8.52 x 10-3 11) 5.05 x 10-2 12) 3.007 x 10-3

13) 254 14) 0.06715)1140

16) 0.38 17) 0.0075318) 56,000

19) 910,000 20) 0.00060821) 859,000

22) 3,331,000 23) 0.0072124) 0.000588

25) 7.7812 x 108 26) the hair

Goals for Today

• 4-6 Squares and Square Roots• Opener- (looking for patterns)• 4-6 Review for Mastery (notes)

• Begin your homework

Extra slides for help if you need it. Please note, the square root signs may be off center.

Vocabularysquare rootprincipal square rootperfect square

The square root of a number is one of the two equal factors of that number. Squaring a nonnegative number and finding the square root of that number are inverse operations.

Because the area of a square can be expressed using an exponent of 2, a number with an exponent of 2 is said to be squared. You read 32 as “three squared.”

3

3

Area = 32

Positive real numbers have two square roots, one positive and one negative. The positive square root, or principle square root, is represented by . The negative square root is represented by – .

A perfect square is a number whose square roots are integers. Some examples of perfect squares are shown in the table.

You can write the square roots of 16 as ±4, which is read as “plus or minus four.”

Writing Math

Additional Example: 1 Finding the Positive and Negative Square Roots of a Number

Find the two square roots of each number.

7 is a square root, since 7 • 7 = 49.

–7 is also a square root, since –7 • (–7) = 49.

10 is a square root, since 10 • 10 = 100.

–10 is also a square root, since –10 • (–10) = 100.

49 = –7–

49 = 7

100 = 10

100 = –10–

A. 49

B. 100The square roots of 49 are ±7.

The square roots of 100 are ±10.

A. 25

Check It Out! Example 1

5 is a square root, since 5 • 5 = 25.

–5 is also a square root, since –5 • (–5) = 25.

12 is a square root, since 12 • 12 = 144.

–12 is also a square root, since –12 • (–12) = 144.

25 = –5–

25 = 5

144 = 12

144 = –12–

Find the two square roots of each number.

B. 144

The square roots of 144 are ±12.

The square roots of 25 are ±5.

132 = 169

The window is 13 inches wide.

Find the square root of 169 to find the width of the window. Use the positive square root; a negative length has no meaning.

Additional Example 2: Application

A square window has an area of 169 square inches. How wide is the window?

So 169 = 13.

Find the square root of 16 to find the width of the table. Use the positive square root; a negative length has no meaning.

Check It Out! Example 2

A square shaped kitchen table has an area of 16 square feet. Will it fit through a van door that has a 5 foot wide opening?

So the table is 4 feet wide, which is less than 5 feet, so it will fit through the van door.

16 = 4

Additional Example 3: Finding the Square Root of a Monomial

Simplify the expression.A.

Write the monomial as a square.

Use the absolute-value symbol.= 12|c|

144c2

144c2 = (12c)2

B. z6

z6 = (z3)2

= |z3|

Write the monomial as a square: z6 = (z3)2

Use the absolute-value symbol.

Additional Example 3: Finding the Square Root of a Monomial

Simplify the expression.

C.

Write the monomial as a square.

10n2 is nonnegative for all values of n. The absolute-value symbol is not needed.

= 10n2

100n4

100n4 = (10n2)2

Check It Out! Example 3

Simplify the expression.A.

Write the monomial as a square.

Use the absolute-value symbol.= 11|r|

121r2

121r2 = (11r)2

B. p8

p8 = (p4)2

= |p4|

Write the monomial as a square: p8 = (p4)2

Use the absolute-value symbol.

Check It Out! Example 3

Simplify the expression.

C.

Write the monomial as a square.

9m2 is nonnegative for all values of m. The absolute-value symbol is not needed.

= 9m2

81m4

81m4 = (9m2)2

Lesson Quiz

±12 ±50

7|p3| z4

5. Ms. Estefan wants to put a fence around 3 sides of a square garden that has an area of 225 ft2. How much fencing does she need?

45 ft

Find the two square roots of each number.

1. 144 2. 2500

Simplify each expression.

3. 49p6 4. z8