<< Chapter < Page Chapter >> Page >

Suppose your calculator has a 10-digit display. Using it to find the square root of 5 will give 2.236067977 . This is the approximate square root of 5 . When we report the answer, we should use the “approximately equal to” sign instead of an equal sign.

5 2.236067978

You will seldom use this many digits for applications in algebra. So, if you wanted to round 5 to two decimal places, you would write

5 2.24

How do we know these values are approximations and not the exact values? Look at what happens when we square them.

2.236067978 2 = 5.000000002 2.24 2 = 5.0176

The squares are close, but not exactly equal, to 5 .

Round 17 to two decimal places using a calculator.

Solution

17
Use the calculator square root key. 4.123105626
Round to two decimal places. 4.12
17 4.12
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Round 11 to two decimal places.

≈ 3.32

Got questions? Get instant answers now!

Round 13 to two decimal places.

≈ 3.61

Got questions? Get instant answers now!

Simplify variable expressions with square roots

Expressions with square root that we have looked at so far have not had any variables. What happens when we have to find a square root of a variable expression?

Consider 9 x 2 , where x 0 . Can you think of an expression whose square is 9 x 2 ?

( ? ) 2 = 9 x 2 ( 3 x ) 2 = 9 x 2 so 9 x 2 = 3 x

When we use a variable in a square root expression, for our work, we will assume that the variable represents a non-negative number. In every example and exercise that follows, each variable in a square root expression is greater than or equal to zero.

Simplify: x 2 .

Solution

Think about what we would have to square to get x 2 . Algebraically, ( ? ) 2 = x 2

x 2
Since ( x ) 2 x
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Simplify: 16 x 2 .

Solution

16 x 2
Since ( 4 x ) 2 = 16 x 2 4 x
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Simplify: 169 y 2 .

13 y

Got questions? Get instant answers now!

Simplify: 81 y 2 .

Solution

81 y 2
Since ( 9 y ) 2 = 81 y 2 9 y
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Simplify: 121 y 2 .

−11 y

Got questions? Get instant answers now!

Simplify: 100 p 2 .

−10 p

Got questions? Get instant answers now!

Simplify: 36 x 2 y 2 .

Solution

36 x 2 y 2
Since ( 6 x y ) 2 = 36 x 2 y 2 6 x y
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Simplify: 100 a 2 b 2 .

10 ab

Got questions? Get instant answers now!

Simplify: 225 m 2 n 2 .

15 mn

Got questions? Get instant answers now!

Use square roots in applications

As you progress through your college courses, you’ll encounter several applications of square roots. Once again, if we use our strategy for applications, it will give us a plan for finding the answer!

Use a strategy for applications with square roots.

  1. Identify what you are asked to find.
  2. Write a phrase that gives the information to find it.
  3. Translate the phrase to an expression.
  4. Simplify the expression.
  5. Write a complete sentence that answers the question.

Square roots and area

We have solved applications with area before. If we were given the length of the sides of a square, we could find its area by squaring the length of its sides. Now we can find the length of the sides of a square if we are given the area, by finding the square root of the area.

If the area of the square is A square units, the length of a side is A units. See [link] .

Area (square units) Length of side (units)
9 9 = 3
144 144 = 12
A A

Mike and Lychelle want to make a square patio. They have enough concrete for an area of 200 square feet. To the nearest tenth of a foot, how long can a side of their square patio be?

Solution

We know the area of the square is 200 square feet and want to find the length of the side. If the area of the square is A square units, the length of a side is A units.

What are you asked to find? The length of each side of a square patio
Write a phrase. The length of a side
Translate to an expression. A
Evaluate A when A = 200 . 200
Use your calculator. 14.142135 ...
Round to one decimal place. 14.1 feet
Write a sentence. Each side of the patio should be 14.1 feet.
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Questions & Answers

find the 15th term of the geometric sequince whose first is 18 and last term of 387
Jerwin Reply
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
virgelyn Reply
hmm well what is the answer
Abhi
how do they get the third part x = (32)5/4
kinnecy Reply
can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Prealgebra' conversation and receive update notifications?

Ask