## Practice Makes Perfect

**Simplify Expressions with Square Roots**

In the following exercises, simplify.

659. \(\sqrt{36}\)

660. \(\sqrt{4}\)

661. \(\sqrt{64}\)

662. \(\sqrt{169}\)

663. \(\sqrt{9}\)

664. \(\sqrt{16}\)

665. \(\sqrt{100}\)

666. \(\sqrt{144}\)

667. \(\sqrt{−4}\)

668. \(\sqrt{−100}\)

669. \(\sqrt{−1}\)

670. \(\sqrt{−121}\)

**Identify Integers, Rational Numbers, Irrational Numbers, and Real Numbers**

In the following exercises, write as the ratio of two integers.

__671__.

ⓐ 5 ⓑ 3.19

672.

ⓐ 8 ⓑ 1.61

__673__.

ⓐ −12−12 ⓑ 9.279

674.

ⓐ −16−16 ⓑ 4.399

In the following exercises, list the ⓐ rational numbers, ⓑ irrational numbers

__675__.

0.75,0.223–,1.391740.75,0.223–,1.39174

676.

0.36,0.94729…,2.528–0.36,0.94729…,2.528–

__677__.

0.45–,1.919293…,3.590.45–,1.919293…,3.59

678.

0.13–,0.42982…,1.8750.13–,0.42982…,1.875

In the following exercises, identify whether each number is rational or irrational.

__679__.

ⓐ 25‾‾‾√25 ⓑ 30‾‾‾√30

680.

ⓐ 44‾‾‾√44 ⓑ 49‾‾‾√49

__681__.

ⓐ 164‾‾‾‾√164 ⓑ 169‾‾‾‾√169

682.

ⓐ 225‾‾‾‾√225 ⓑ 216‾‾‾‾√216

In the following exercises, identify whether each number is a real number or not a real number.

__683__.

ⓐ −81‾‾‾√−81 ⓑ −121‾‾‾‾‾√−121

684.

ⓐ −64‾‾‾√−64 ⓑ −9‾‾‾√−9

__685__.

ⓐ −36‾‾‾‾√−36 ⓑ −144‾‾‾‾√−144

686.

ⓐ −49‾‾‾‾√−49 ⓑ −144‾‾‾‾√−144

In the following exercises, list the ⓐ whole numbers, ⓑ integers, ⓒ rational numbers, ⓓ irrational numbers, ⓔ real numbers for each set of numbers.

__687__.

−8,0,1.95286…,125,36‾‾‾√,9−8,0,1.95286…,125,36,9

688.

−9,−349,−9‾√,0.409–,116,7−9,−349,−9,0.409–,116,7

__689__.

−100‾‾‾‾√,−7,−83,−1,0.77,314−100,−7,−83,−1,0.77,314

690.

−6,−52,0,0.714285———,215,14‾‾‾√−6,−52,0,0.714285———,215,14

**Locate Fractions on the Number Line**

In the following exercises, locate the numbers on a number line.

__691__.

34,85,10334,85,103

692.

14,95,11314,95,113

__693__.

310,72,116,4310,72,116,4

694.

710,52,138,3710,52,138,3

__695__.

25,−2525,−25

696.

34,−3434,−34

__697__.

34,−34,123,−123,52,−5234,−34,123,−123,52,−52

698.

15,−25,134,−134,83,−8315,−25,134,−134,83,−83

In the following exercises, order each of the pairs of numbers, using < or >.

__699__.

−1___−14−1___−14

700.

−1___−13−1___−13

__701__.

−212___−3−212___−3

702.

−134___−2−134___−2

__703__.

−512___−712−512___−712

704.

−910___−310−910___−310

__705__.

−3___−135−3___−135

706.

−4___−236−4___−236

Locate Decimals on the Number Line In the following exercises, locate the number on the number line.

__707__.

0.8

708.

−0.9−0.9

__709__.

−1.6−1.6

710.

3.1

In the following exercises, order each pair of numbers, using < or >.

__711__.

0.37___0.630.37___0.63

712.

0.86___0.690.86___0.69

__713__.

0.91___0.9010.91___0.901

714.

0.415___0.410.415___0.41

__715__.

−0.5___−0.3−0.5___−0.3

716.

−0.1___−0.4−0.1___−0.4

__717__.

−0.62___−0.619−0.62___−0.619

718.

−7.31___−7.3−7.31___−7.3

### Everyday Math

__719__.

Field trip All the 5th graders at Lincoln Elementary School will go on a field trip to the science museum. Counting all the children, teachers, and chaperones, there will be 147 people. Each bus holds 44 people.

ⓐ How many busses will be needed?

ⓑ Why must the answer be a whole number?

ⓒ Why shouldn’t you round the answer the usual way, by choosing the whole number closest to the exact answer?

720.

Child care Serena wants to open a licensed child care center. Her state requires there be no more than 12 children for each teacher. She would like her child care center to serve 40 children.

ⓐ How many teachers will be needed?

ⓑ Why must the answer be a whole number?

ⓒ Why shouldn’t you round the answer the usual way, by choosing the whole number closest to the exact answer?

### Writing Exercises

__721__.

In your own words, explain the difference between a rational number and an irrational number.

722.

Explain how the sets of numbers (counting, whole, integer, rational, irrationals, reals) are related to each other.

### Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objective of this section.

ⓑ On a scale of 1−10,1−10, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?