Lesson 9-1 Pages 436-440

Squares and Square Roots

PA Lesson Check 7-Ch7

Read Pages 436-438

What you will learn!1. How to find squares and square roots.

2. How to estimate square roots.

Perfect SquarePerfect Square

Square rootSquare rootRadical signRadical sign

What you really need to know!

A perfect square is the square of a whole number.

A square root of a number is one of two equal factors of the number.

Every positive number has a positive square root and a negative square root.The square root of a negative number such as –25, is not real because the square of a number is never negative.

What you really need to know!

Square Square Root

Example 1:

Find the square root:

64Since 82 = 64,

864

Example 1b:

Find the square root:

121Since 112 = 121,

11121

Example 1c:

Find the square root:

4Since 22 = 4 and (-2)2 = 4,

2 and 24

Example 2:

Use a calculator to fine the square root to the nearest tenth.

233312714.7958315223

4.8

Example 2b:

Use a calculator to fine the square root to the nearest tenth.

463125276.7823299846

-6.8

Example 3:

Estimate the square root to the nearest whole number.

22The perfect squares are:

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, ...

22 is between 16 and 25.

The perfect squares are:

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, ...

525 and 416

22

22 is closer to 25. So 5 is the best estimate for the square root of 22.

522 The perfect squares are:

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, ...

Example 3b:

Estimate the square root to the nearest whole number.

319The perfect squares are:

..., 169, 196, 225, 256, 289, 324, 361, ...

319 is between 289 and 324.

81324 and 17289

The perfect squares are:

..., 169, 196, 225, 256, 289, 324, 361, ...

319

319 is closer to 325. So 18 is the best estimate for the square root of 319.

18319 The perfect squares are:

..., 169, 196, 225, 256, 289, 324, 361, ...

Example 4:

where D is the distance in miles and A is the altitude, or height, in feet.

To estimate how far you can see from a point above the horizon, you can use the formula:

AD 22.1

Example 4:

AD 22.1

The observations deck at the Seattle Space Needle is 520 feet above the ground. On a clear day, about how far could a tourist see? Round to the nearest tenth.

AD 22.1

52022.1 D01982822.803508522.1 D

7241927.8202803D27.8miD

Page 438

Guided Practice

#’s 4-11

Pages 436-438 with someone at home and

study examples!

Read:

Homework: Pages 439-440

#’s 12-56 even, 71-80

Lesson Check 9-1

Homework: Pages 439-440

#’s 12-56 even

#’s 59, 60 and 71-74

Page

745

Lesson 9-1

Lesson Check 9-1