<< Chapter < Page Chapter >> Page >

The product rule for simplifying square roots

If a and b are nonnegative, the square root of the product a b is equal to the product of the square roots of a and b .

a b = a b

Given a square root radical expression, use the product rule to simplify it.

  1. Factor any perfect squares from the radicand.
  2. Write the radical expression as a product of radical expressions.
  3. Simplify.

Using the product rule to simplify square roots

Simplify the radical expression.

  1. 300
  2. 162 a 5 b 4

  1. 100 3 Factor perfect square from radicand . 100 3 Write radical expression as product of radical expressions . 10 3 Simplify .

  2. 81 a 4 b 4 2 a Factor perfect square from radicand . 81 a 4 b 4 2 a Write radical expression as product of radical expressions . 9 a 2 b 2 2 a Simplify .
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Simplify 50 x 2 y 3 z .

5 | x | | y | 2 y z . Notice the absolute value signs around x and y ? That’s because their value must be positive!

Got questions? Get instant answers now!

Given the product of multiple radical expressions, use the product rule to combine them into one radical expression.

  1. Express the product of multiple radical expressions as a single radical expression.
  2. Simplify.

Using the product rule to simplify the product of multiple square roots

Simplify the radical expression.
12 3

12 3 Express the product as a single radical expression . 36 Simplify . 6

Got questions? Get instant answers now!
Got questions? Get instant answers now!

Simplify 50 x 2 x assuming x > 0.

10 | x |

Got questions? Get instant answers now!

Using the quotient rule to simplify square roots

Just as we can rewrite the square root of a product as a product of square roots, so too can we rewrite the square root of a quotient as a quotient of square roots, using the quotient rule for simplifying square roots. It can be helpful to separate the numerator and denominator of a fraction under a radical so that we can take their square roots separately. We can rewrite 5 2 as 5 2 .

The quotient rule for simplifying square roots

The square root of the quotient a b is equal to the quotient of the square roots of a and b , where b 0.

a b = a b

Given a radical expression, use the quotient rule to simplify it.

  1. Write the radical expression as the quotient of two radical expressions.
  2. Simplify the numerator and denominator.

Using the quotient rule to simplify square roots

Simplify the radical expression.

5 36

5 36 Write as quotient of two radical expressions . 5 6 Simplify denominator .

Got questions? Get instant answers now!
Got questions? Get instant answers now!

Simplify 2 x 2 9 y 4 .

x 2 3 y 2 . We do not need the absolute value signs for y 2 because that term will always be nonnegative.

Got questions? Get instant answers now!

Using the quotient rule to simplify an expression with two square roots

Simplify the radical expression.

234 x 11 y 26 x 7 y

234 x 11 y 26 x 7 y Combine numerator and denominator into one radical expression . 9 x 4 Simplify fraction . 3 x 2    Simplify square root .

Got questions? Get instant answers now!
Got questions? Get instant answers now!

Simplify 9 a 5 b 14 3 a 4 b 5 .

b 4 3 a b

Got questions? Get instant answers now!

Adding and subtracting square roots

We can add or subtract radical expressions only when they have the same radicand and when they have the same radical type such as square roots. For example, the sum of 2 and 3 2 is 4 2 . However, it is often possible to simplify radical expressions, and that may change the radicand. The radical expression 18 can be written with a 2 in the radicand, as 3 2 , so 2 + 18 = 2 + 3 2 = 4 2 .

Given a radical expression requiring addition or subtraction of square roots, solve.

  1. Simplify each radical expression.
  2. Add or subtract expressions with equal radicands.

Questions & Answers

how does Neisseria cause meningitis
Nyibol Reply
what is microbiologist
Muhammad Reply
what is errata
Muhammad
is the branch of biology that deals with the study of microorganisms.
Ntefuni Reply
What is microbiology
Mercy Reply
studies of microbes
Louisiaste
when we takee the specimen which lumbar,spin,
Ziyad Reply
How bacteria create energy to survive?
Muhamad Reply
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Muhamad
they make spores
Louisiaste
what is sporadic nd endemic, epidemic
Aminu Reply
the significance of food webs for disease transmission
Abreham
food webs brings about an infection as an individual depends on number of diseased foods or carriers dully.
Mark
explain assimilatory nitrate reduction
Esinniobiwa Reply
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
Elkana
Examples of thermophilic organisms
Shu Reply
Give Examples of thermophilic organisms
Shu
advantages of normal Flora to the host
Micheal Reply
Prevent foreign microbes to the host
Abubakar
they provide healthier benefits to their hosts
ayesha
They are friends to host only when Host immune system is strong and become enemies when the host immune system is weakened . very bad relationship!
Mark
what is cell
faisal Reply
cell is the smallest unit of life
Fauziya
cell is the smallest unit of life
Akanni
ok
Innocent
cell is the structural and functional unit of life
Hasan
is the fundamental units of Life
Musa
what are emergency diseases
Micheal Reply
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life
Lubega
Heyy Lubega hussein where are u from?
_Adnan
en français
Adama
which site have a normal flora
ESTHER Reply
Many sites of the body have it Skin Nasal cavity Oral cavity Gastro intestinal tract
Safaa
skin
Asiina
skin,Oral,Nasal,GIt
Sadik
How can Commensal can Bacteria change into pathogen?
Sadik
How can Commensal Bacteria change into pathogen?
Sadik
all
Tesfaye
by fussion
Asiina
what are the advantages of normal Flora to the host
Micheal
what are the ways of control and prevention of nosocomial infection in the hospital
Micheal
what is inflammation
Shelly Reply
part of a tissue or an organ being wounded or bruised.
Wilfred
what term is used to name and classify microorganisms?
Micheal Reply
Binomial nomenclature
adeolu
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
Practice Key Terms 6

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

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

Ask