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

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$180$ calories per $8$ ounces

$90$ pounds per $7.5$ square inches

$\frac{90\phantom{\rule{0.2em}{0ex}}\text{pounds}}{7.5\phantom{\rule{0.2em}{0ex}}\text{square inches}}$

$126$ miles in $4$ hours

$\text{612.50}$ for $35$ hours

$\frac{\text{612.50}}{35\phantom{\rule{0.2em}{0ex}}\text{hours}}$

Find Unit Rates

In the following exercises, find the unit rate.

$180$ calories per $8$ ounces

$90$ pounds per $7.5$ square inches

12 pounds/sq.in.

$126$ miles in $4$ hours

$\text{612.50}$ for $35$ hours

$17.50/hour Find Unit Price In the following exercises, find the unit price. t-shirts: $3$ for $\text{8.97}$ Highlighters: $6$ for $\text{2.52}$$0.42

An office supply store sells a box of pens for $\text{11}.$ The box contains $12$ pens. How much does each pen cost?

Anna bought a pack of $8$ kitchen towels for $\text{13.20}.$ How much did each towel cost? Round to the nearest cent if necessary.

$1.65 In the following exercises, find each unit price and then determine the better buy. Shampoo: $12$ ounces for $\text{4.29}$ or $22$ ounces for $\text{7.29}?$ Vitamins: $60$ tablets for $\text{6.49}$ or $100$ for $\text{11.99}?$$0.11, $0.12; 60 tablets for$6.49

Translate Phrases to Expressions with Fractions

In the following exercises, translate the English phrase into an algebraic expression.

$535$ miles per $h\phantom{\rule{0.2em}{0ex}}\text{hours}$

$a$ adults to $45$ children

$\frac{a\phantom{\rule{0.2em}{0ex}}\text{adults}}{45\phantom{\rule{0.2em}{0ex}}\text{children}}$

the ratio of $4y$ and the difference of $x$ and $10$

the ratio of $19$ and the sum of $3$ and $n$

$\frac{19}{3+n}$

## Simplify and Use Square Roots

Simplify Expressions with Square Roots

In the following exercises, simplify.

$\sqrt{64}$

$\sqrt{144}$

12

$-\sqrt{25}$

$-\sqrt{81}$

−9

$\sqrt{-9}$

$\sqrt{-36}$

not a real number

$\sqrt{64}+\sqrt{225}$

$\sqrt{64+225}$

17

Estimate Square Roots

In the following exercises, estimate each square root between two consecutive whole numbers.

$\sqrt{28}$

$\sqrt{155}$

$12<\sqrt{155}<13$

Approximate Square Roots

In the following exercises, approximate each square root and round to two decimal places.

$\sqrt{15}$

$\sqrt{57}$

7.55

Simplify Variable Expressions with Square Roots

In the following exercises, simplify. (Assume all variables are greater than or equal to zero.)

$\sqrt{{q}^{2}}$

$\sqrt{64{b}^{2}}$

8 b

$-\sqrt{121{a}^{2}}$

$\sqrt{225{m}^{2}{n}^{2}}$

15 mn

$-\sqrt{100{q}^{2}}$

$\sqrt{49{y}^{2}}$

7 y

$\sqrt{4{a}^{2}{b}^{2}}$

$\sqrt{121{c}^{2}{d}^{2}}$

11 cd

Use Square Roots in Applications

In the following exercises, solve. Round to one decimal place.

Art Diego has $225$ square inch tiles. He wants to use them to make a square mosaic. How long can each side of the mosaic be?

Landscaping Janet wants to plant a square flower garden in her yard. She has enough topsoil to cover an area of $30$ square feet. How long can a side of the flower garden be?

5.5 feet

Gravity A hiker dropped a granola bar from a lookout spot $576$ feet above a valley. How long did it take the granola bar to reach the valley floor?

Accident investigation The skid marks of a car involved in an accident were $216$ feet. How fast had the car been going before applying the brakes?

72 mph

## Chapter practice test

Write six and thirty-four thousandths as a decimal.

Write $1.73$ as a fraction.

$1\frac{73}{100}$

Write $\frac{5}{8}$ as a decimal.

Round $16.749$ to the nearest tenth hundredth whole number

1. 16.7
2. 16.75
3. 17

Write the numbers $\frac{4}{5},-0.1,0.804,\frac{2}{9},-7.4,0.21$ in order from smallest to largest.

In the following exercises, simplify each expression.

$15.4+3.02$

18.42

$20-5.71$

$\left(0.64\right)\left(0.3\right)$

0.192

$\left(-4.2\right)\left(100\right)$

$0.96÷\left(-12\right)$

−0.08

$-5÷0.025$

$-0.6÷\left(-0.3\right)$

2

${\left(0.7\right)}^{2}$

$24÷\left(0.1+0.02\right)$

200

$4\left(10.3-5.8\right)$

$1.6+\frac{3}{8}$

1.975

$\frac{2}{3}\left(14.65-4.6\right)$

In the following exercises, solve.

$m+3.7=2.5$

−1.2

$\frac{h}{0.5}=4.38$

$-6.5y=-57.2$

8.8

$1.94=a-2.6$

Three friends went out to dinner and agreed to split the bill evenly. The bill was $\text{79.35}.$ How much should each person pay?

$26.45 A circle has radius $12.$ Find the circumference and area. $\text{[}\text{Use}\phantom{\rule{0.2em}{0ex}}3.14\phantom{\rule{0.2em}{0ex}}\text{for}\phantom{\rule{0.2em}{0ex}}\pi \text{.]}$ The ages, in months, of $10$ children in a preschool class are: $55$ , $55$ , $50$ , $51$ , $52$ , $50$ , $53$ , $51$ , $55$ , $49$ Find the mean median mode 1. 59 2. 51.5 3. 55 Of the $16$ nurses in Doreen’s department, $12$ are women and $4$ are men. One of the nurses will be assigned at random to work an extra shift next week. Find the probability a woman nurse will be assigned the extra shift. Convert the fraction to a decimal. Find each unit price and then the better buy. Laundry detergent: $64$ ounces for $\text{10.99}$ or $48$ ounces for $\text{8.49}$ 64 ounces for$10.99 is the better buy

In the following exercises, simplify.

$\sqrt{36+64}$

$\sqrt{144{n}^{2}}$

12 n

Estimate $\sqrt{54}$ to between two whole numbers.

Yanet wants a square patio in her backyard. She has $225$ square feet of tile. How long can a side of the patio be?

15 feet

where we get a research paper on Nano chemistry....?
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
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
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
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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?