Question

In your own words, what are radical expressions? What is the process we follow when adding, subtracting, multiplying, and dividing radical expressions? In your answer, demonstrate the process for each one with your own example.

Answer 1

iraqichick lol why'd you chose this ?

Answer 2

i didnt choose it the teacher posted it!!

Answer 3

ah okay lol sorry can't help you with this

Answer 4

A radical expression is an expression which contains a radical sign(√), which is called a square root.

Answer 5

\[2\sqrt{5} + 3\sqrt{5} \to \Large 5\sqrt{5}\]

Answer 6

\[3\sqrt{5}-2\sqrt{5}\to \Huge \sqrt{5}\]

Answer 7

that was for addition and subtraction.

Answer 8

thats it?? i need like 150 to 200 words! :/

Answer 9

you better Google this thing

Answer 10

:/

Answer 11

no, there is still divison & multiplication.

Oh, i thought you wanted 50 like everytime.

Answer 12

no no this needs to be long cuz its the main question

Answer 13

wow, Ok.
so that must be an essay!!

Answer 14

not really cuz its only 150 to 200 words so its a bit shorter lol she wants details and an example

Answer 15

ONLY 150. lol. Ok.

Answer 16

Let me make some stories now! ;)

Answer 17

lol ok :D

Answer 18

Thinking.

Answer 19

lol i would help u think but my brain hurts lol

Answer 20

u want to see an example of what someone elese wrote?

Answer 21

lol, Sure. post it.

Answer 22

Radical expressions are square roots of monomials, binomials, or polynomials. One way of simplifying radical expressions is to break down the expression into perfect squares multiplying each other. A perfect square, such as 4, 9, 16 or 25, has a whole number square root. Simplifying radical expressions becomes especially important in Geometry when solving formulas and in using the Pythagorean Theorem.

Adding and subtracting radical expressions is similar to combining like terms: if two terms are multiplying the same radical expression, their coefficients can be summed. Some problems will not start with the same roots but the terms can be added after simplifying one or both radical expressions. Adding like radicals appears later in Algebra and frequently in Geometry.

√18+√24-√8

√9*2+√4*6-√4*2

3√2+2√6-2√2

√2+2√6

When multiplying radical expressions, it is helpful to remember that only terms "inside" the radicals can be multiplied and only the terms "outside" the radical can be multiplied together. After multiplying radicals, check to see if any perfect squares can be factored out to simplify the radical expression. Multiplying radicals is used to rationalize radicals and in Geometry.

(√2+√3)(√5+√7)= (FOIL)
√10+√14+√15+√21
Finally, for division there is a trick
1/(√5+√2)
We rationalize the denominator by multiplying top and bottom by √5-√2.
When we do this, the numerator becomes √5-√2 while the denominator becomes (√5+√2) (√5-√2).
This has the form (a+b) (a-b) which equals a squared minus b squared which in this case is 5-2 =3. So we get (√5-√2)/3 as our answer.

Answer 23

wow, that's long.

Answer 24

and another person put....
A radical expression is an expression written with a radical sign (√). A radical expression consist of the radical symbol, radicands (the entire expression inside the radical sign), radicands can be broken into the base, the power and the index.

We follow the same distributive laws and the simplification methods when we add, subtract, multiply, and divide radical expressions. We just need to be careful of knowing when one of these steps will be applied.

When adding a radical expression, we must first look at the radicand, if these are equivalent, then we just add the outside index, i.e. 2√x + 5√x = 7√x

Another example would be:

√50 + √18 =
√50 = √25*√2 or 5√2
√18 = √9*√2 or 3√2
so then we have:
5√2 + 3√2 = 8√2

When subtracting, the same operational methods need to be considered

√50 - √18 =
√50 = √25*√2 or 5√2
√18 = √9*√2 or 3√2
5√2 - 3√2 = 2√2

When multiplying:
√12 * √10
Because 12 can be simplified with a perfect square we can:
√4*√3 = 2√3
so then we have:
2√3 * √10 = 2√30 (we will only multiply the base by each other)

Dividing:
√24/3 = √8 = √4*√2 = 2√2

There will be radical expressions that cannot be simplified, for example

Answer 25

√20/4 = √5 - 5 cannot be simplified, so this would be the final result

Answer 26

what is -5 u wrote?

Answer 27

that the ending part to the thing i posted

Answer 28

ishaan u wrote all that or googled it??

Answer 29

lol of course Google

Answer 30

lol, UoP guys don't like googling on this! :O

Answer 31

UoP?

Answer 32

trust me we google we just cant copy and paste answers from there cuz our teachers are featheres!!!

Answer 33

ah Okay Lol I will thing about the answers I means essay I will try

Answer 34

but first answer my question what did you type for featheres

Answer 35

wat the heck?? i wrote a bad word it changed it to feathers??

Answer 36

I have been typing so many bad word but I am not able to get what turns into feather

Answer 37

ah write it like this S H I T

Answer 38

the b word hahahahha

Answer 39

feather

Answer 40

b i t c h e s

Answer 41

ah I got it thanks

Answer 42

ahhhhh

Answer 43

thats cute loool

Answer 44

pellet

Answer 45

hahahaha how funny it changes bad words

Answer 46

thats good though cuz lil kids come on here

Answer 47

Radical expressions are square roots of monomials, binomials, or polynomials. One way of simplifying radical expressions is to break down the expression into perfect squares multiplying each other. A perfect square, such as 4, 9, 16 or 25, has a whole number square root. Simplifying radical expressions becomes especially important in Geometry when solving formulas and in using the Pythagorean Theorem.

We follow the same distributive laws and the simplification methods when we add, subtract, multiply, and divide radical expressions. We just need to be careful of knowing when one of these steps will be applied.

Addition Example:
sqrt(108) + sqrt(12)
= sqrt(3*36) + sqrt(3*4)
= 6sqrt3 + 2sqrt3
= 8 sqrt 3
Subtraction:
sqrt(108) - sqrt(12)
= sqrt(3*36) - sqrt(3*4)
= 6sqrt3 - 2sqrt3
= 4 sqrt 3
To multiply or divide roots, you don’t have to have like roots, just like with polynomials, you didn’t have to have like powers. You multiply or divide the values inside the roots separately from the values outside the roots.
Division Example:
sqrt(8) / sqrt(2)
= sqrt(8/2)
= sqrt(4)
= 2
Multiplication:
sqrt(8) * sqrt(2)
= sqrt(8*2)
= sqrt(16)
= 4

Answer 48

lol that is a mix of all three articles

Answer 49

They won't get this even if they Google it

Answer 50

I am pretty sure

Answer 51

Googled^

Answer 52

ah Mixture of Googled Articles

Answer 53

wat did u come up with saif??

Answer 54

Just gve me last 10minutes.

Answer 55

tyt

Answer 56

Taken. ;)

Answer 57

Radical Expressions

Radical expressions are square root of Algebraic expressions like monomials, polynomials ,etc. For example \(\sqrt{1+x^2}\) is a 'Radical Expression'.
Addition, Subtraction, Division, Multiplication of Radical expressions follows same rules as for Algebraic expressions.

1. Addition of Radical Expressions
Let us consider an example involving Radicals \(\sqrt5\) and \(4\sqrt5\).
\[\sqrt5 + 4\sqrt5 \:\:\:\:\:\:\text{(Taking \(\sqrt5\) common)}=> \sqrt5(1 + 4) = 5 \sqrt5\]
If there had been an algebraic sum or Addition we would have followed the same process.
For Example. Addition of 3x and 4x
3x + 4x = x(4 +3 ) = 7x

2. Subtraction
Subtraction is same as Addition just a change of sign to confuse us.
Subtraction of \(3\sqrt3 \) and \(\sqrt3\)
\[ \sqrt3 - 3 \sqrt3 \:\:\:\:\text{(Taking \(\sqrt3\) common )} = \sqrt3(1 - 3 ) = -2\sqrt3\]

Ah I think this much is enough in same you can write about Multiplication and Division or Copy some examples from NET ; )

Answer 58

and the above is written by me not some Googled material

Answer 59

ah you here iraqichick?

Answer 60

ah no...I really typed it all don't tell me you left your computer online ah nevermind

Answer 61

im back sorry

Answer 62

my daughter locked my computer i couldnt fix it

Answer 63

you have a daughter !!!!!!!! lol I thought you were in school

Answer 64

i am im 22 years old and my daughert is 2

Answer 65

Cool : )
well did the above thing helped you

Answer 66

i dont want it to helpn me i just need an answer cuz i had thtis class!!