# 5.7 Simplify and use square roots  (Page 6/8)

 Page 6 / 8

## Writing exercises

Why is there no real number equal to $\sqrt{-64}?$

What is the difference between ${9}^{2}$ and $\sqrt{9}?$

Answers will vary. 9 2 reads: “nine squared” and means nine times itself. The expression $\sqrt{9}$ reads: “the square root of nine” which gives us the number such that if it were multiplied by itself would give you the number inside of the square root.

## Self check

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

Overall, after looking at the checklist, do you think you are well-prepared for the next Chapter? Why or why not?

## Decimals

Name Decimals

In the following exercises, name each decimal.

$0.8$

$0.375$

three hundred seventy-five thousandths

$0.007$

$5.24$

five and twenty-four hundredths

$-12.5632$

$-4.09$

negative four and nine hundredths

Write Decimals

In the following exercises, write as a decimal.

three tenths

nine hundredths

0.09

twenty-seven hundredths

ten and thirty-five thousandths

10.035

negative twenty and three tenths

negative five hundredths

−0.05

Convert Decimals to Fractions or Mixed Numbers

In the following exercises, convert each decimal to a fraction. Simplify the answer if possible.

$0.43$

$0.825$

$\frac{33}{40}$

$9.7$

$3.64$

$3\frac{16}{25}$

Locate Decimals on the Number Line

Locate the following decimals on a number line.

$\phantom{\rule{0.2em}{0ex}}0.6$

$\phantom{\rule{0.2em}{0ex}}-0.9$

$\phantom{\rule{0.2em}{0ex}}2.2$

$\phantom{\rule{0.2em}{0ex}}-1.3$

Order Decimals

In the following exercises, order each of the following pairs of numbers, using $<$ or $\text{>.}$

$0.6___0.8$

<

$0.2___0.15$

$0.803____0.83$

<

$-0.56____-0.562$

Round Decimals

In the following exercises, round each number to the nearest:

hundredth

tenth

whole number.

$12.529$

1. 12.53
2. 12.5
3. 13

$4.8447$

$5.897$

1. 5.90
2. 5.9
3. 6

## Decimal Operations

In the following exercises, add or subtract.

$5.75+8.46$

$32.89-8.22$

24.67

$24-19.31$

$10.2+14.631$

24.831

$-6.4+\left(-2.9\right)$

$1.83-4.2$

−2.37

Multiply Decimals

In the following exercises, multiply.

$\left(0.3\right)\left(0.7\right)$

$\left(-6.4\right)\left(0.25\right)$

−1.6

$\left(-3.35\right)\left(-12.7\right)$

$\left(15.4\right)\left(1000\right)$

15,400

Divide Decimals

In the following exercises, divide.

$0.48÷6$

$4.32÷24$

0.18

$\text{6.29}÷12$

$\left(-0.8\right)÷\left(-0.2\right)$

4

$1.65÷0.15$

$9÷0.045$

200

Use Decimals in Money Applications

In the following exercises, use the strategy for applications to solve.

Miranda got $\text{40}$ from her ATM. She spent $\text{9.32}$ on lunch and $\text{16.99}$ on a book. How much money did she have left? Round to the nearest cent if necessary.

Jessie put $8$ gallons of gas in her car. One gallon of gas costs $\text{3.528.}$ How much did Jessie owe for all the gas?

$28.22 A pack of $16$ water bottles cost $\text{6.72.}$ How much did each bottle cost? Alice bought a roll of paper towels that cost $\text{2.49.}$ She had a coupon for $\text{0.35}$ off, and the store doubled the coupon. How much did Alice pay for the paper towels?$1.79

## Decimals and Fractions

Convert Fractions to Decimals

In the following exercises, convert each fraction to a decimal.

$\frac{3}{5}$

$\frac{7}{8}$

0.875

$-\frac{19}{20}$

$-\frac{21}{4}$

−5.25

$\frac{1}{3}$

$\frac{6}{11}$

$0.\stackrel{\text{—}}{54}$

Order Decimals and Fractions

In the following exercises, order each pair of numbers, using $<$ or $\text{>.}$

$\frac{1}{2}___0.2$

$\frac{3}{5}___0.$

>

$-\frac{7}{8}___-0.84$

$-\frac{5}{12}___-0.42$

>

$0.625___\frac{13}{20}$

$0.33___\frac{5}{16}$

>

In the following exercises, write each set of numbers in order from least to greatest.

$\frac{2}{3},\frac{17}{20},0.65$

$\frac{7}{9},0.75,\frac{11}{15}$

$\frac{11}{15},0.75,\frac{7}{9}$

Simplify Expressions Using the Order of Operations

are nano particles real
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
no can't
Lohitha
where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Jeannette has $5 and$10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
What is the expressiin for seven less than four times the number of nickels
How do i figure this problem out.
how do you translate this in Algebraic Expressions
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?