ESTIMATING ROOTS

MATH 8

Warm Up Questions

Evaluate without a calculator

49

1

343

5

19

5

9

27

Estimating Square Roots

Memorize the whole number roots!

1 6 11 16

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2 7 12 17

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3 8 13 18

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4 9 14 19

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5 10 15 20

Irrational Number

a number that can not be written as a ratio of two integers (fraction)

a number that when expanded to a decimal will go on indefinitely

without forming a pattern

Between which two consecutive integers is each square root?

We can be more precise by estimating the roots to the tenths place

Steps for estimating a square root to the tenths place

Determine which two perfect squares the number falls between, write down the lower of the two as the whole number part of the estimate

Determine the distance from the number to the two perfect squares

- if it is closer to the lower, then the decimal will be .1 .2 or .3

- if it is about midway between, then the decimal will be .4 .5 or .6

- if it is closer to the higher, then the decimal will be .7 .8 or .9

Check your estimate by multiplying the number by itself. It must be close to the original number under the radical symbol

Estimate each square root to the tenths place

closer to 9

which is close to 84

closer to 12

If your estimate is

within one-tenth of

the answer on the Key

it can be marked correct

Estimate each square root to the tenths place

closer to 18

almost halfway between

Compare the following roots by filling in each blank with

> , <, or = to make the statement true

>

3

9

16

−4

<

<

Place each of the points on the number line given

A

=5

B

=6

C

D

E

Order the set of numbers from least to greatest

=14

=1.85

185%

13.5

14.7

When ordering use the given numbers as your answers

How do you increase the accuracy of your estimates?

12.96

13.0321

13.003236

13.00035136

12.9999908025

13.0000001769

How close to 13 are the results?

they get closer as you include more decimal places