3.) Explain why we always get an integer when multiplying a radical expression by its conjugate? Provide your own appropriate example with supporting work that matches your explanation.

Answers

Answer 1

By answering the above question, we may state that by equation Once more, we can observe that the two conjugates' product is an integer.

What is equation?

Using the equals notation (=) to indicate equivalence, a math equation links two statements. Algebraic equations prove the equality of three mathematical expressions by a mathematical assertion.

The equal sign, for example, provides a gap between the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. You can use a mathematical formula to understand the connection between the two phrases that are inscribed on opposite sides of a letter. Most of the time, the symbol and the particular software match. e.g., 2x - 4 = 2 is an example.

An integer is always obtained when a radical expression is multiplied by its conjugate since the product has the form[tex]a^2 -b^2[/tex], where a and b are rational numbers. This is so that we may obtain the difference of the squares of the two terms within the radical when we multiply the two conjugates.

Consider the radical expression [tex]\sqrt3 - \sqrt2[/tex] and its conjugate,  [tex]\sqrt3 - \sqrt2[/tex] , to understand this. These two expressions can be multiplied as follows:

[tex]\sqrt{\sqrt3 - \sqrt2\\[/tex]

[tex]\sqrt{(\sqrt3 - \sqrt2) ((\sqrt(3 + \sqrt(2)))} = 3 - \sqrt(2 ) = 1$$[/tex]

As a result, we can observe that the two conjugates' product is an integer.

The radical phrase [tex]\sqrt5 - \sqrt3[/tex] and its conjugate, [tex]\sqrt5 +\sqrt3[/tex] , serve as another illustration.

[tex](\sqrt5 -\sqrt3)[/tex]

[tex](\sqrt(5) + \sqrt(3)) = \sqrt(5) \times \sqrt(5) + \sqrt(5) \times \sqrt(3) - \sqrt(3) \times \sqrt(3)[/tex]

[tex](\sqrt5 - \sqrt3)( \sqrt 5+ \sqrt3) = 5 - 3 = 2[/tex]

Once more, we can observe that the two conjugates' product is an integer.

To know more about equation visit:

brainly.com/question/649785

#SPJ1


Related Questions

each dance class in 3/4 hours it takes 7 1/2 hours to learn a dance routine which statement is true ?

Answers

Step-by-step explanation:

Answer:

10 dance class

Step-by-step explanation:

The correct option is (d) a student needs to take 10 dance classes to learn the routine. Step-by-step explanation: Given that each dance class is hour and a student takes hours to learn a dance routine. We are to select the TRUE statement. Thus, a student needs 10 dance classes to learn the dance routine.

Which of the following equations has a positive slope and a negative y intercept A.y=3.5x
B.y=1/4x+7
C.y=7.5x-2
D.y=-5x-8

Answers

Answer:

C

Step-by-step explanation:

Because 7.5 is a positive and that is the slope and -2 is a negative and that is the y intercept.

PLEASE HELP I will mark brainliest if you explain what you got and how you got it

Answers

Answer:

m=-2 b=0

Step-by-step explanation:

first, in order to understand anything, you gotta know what y=mx+b means :)

first, m is just there so you can substitute it for a number. x represents the slope, and b represents the y-intercept, which you also substitute for a number.

so in y= -2x, there's no y intercept, because there is no number that represents the y intercept.

so if we use y=mx+b, we can just substitute the numbers.

which would be, y= -2.

PLEASE HELP ME WITH THIS GUYS!!

Answers

Answer:

C

Step-by-step explanation:

So they bought 2 sneakers. A pair of sneakers cost $6.49. Multiply that by 2, and you get $12.98.

Then they bought a pair of flip flops. So one pair is $0.99. Add that to the $12.98 you got and now you have $13.97.

They also got a pair of flats. One pair is $7.19, so add that to your $13.97 and you now have $21.16.

They also have to pay $1.75 tax, meaning you add that to the $21.16 you have which makes $22.91 total.

But they said how much change they would get from $30 so we're not done yet. So subtract $22.91 from $30 and your answer will be $7.09 which is C.

Hey please help, I'm pretty sure it's C, but I'm not sure if it's a also

Answers

Answer:

It is only C

Step-by-step explanation:

The only answer for this is C

The correct option is option C i.e. "If the ratio of the arc length to r is 1, then the measure of θ is 1 radians".

What is Arc length?

The arc length is defined as the interspace between the two points along a section of a curve.

Here,  we know that,

angle = arc length / radius    ............(i)

If  arc length / radius = 1   ............(ii)

then from eq. (i) and (ii), we get

angle = 1

θ = 1

Thus, The correct option is option C i.e. "If the ratio of the arc length to r is 1, then the measure of θ is 1 radians".

Learn more about arc length from:

https://brainly.com/question/16403495

#SPJ2

(20x^2 – 3x – 9)/(4x – 3)

Answers

Answer:

5x+3

Step-by-step explanation:

Rewrite the expression to  20x^2-3x-9/4x-3

Factor 20x^2+12x-15x-9/4x-3

Factor 4x*5x+3-3(5x+3)/4x-3

Factor (5x+3)*(4x-3)/4x-3

Solution then becomes 5x+3 as stated above

5(2x+1)-2x

How to solve

Answers

Answer:

8x + 5

Step-by-step explanation:

5 * (2x+1) = 10x +5

10x + 5 -2x

8x + 5

What can u multiply by 8.6
then divide by two to get
32.25

Answers

8.6 * 7.5 divided by 2 is 32.25

Answer:

umm

Step-by-step explanation:

32.25*2=64.50

64.50/8.6=7.5

so the answer is yes

HELP ME PLEASEEEEE I NEEED HELP AGAIN HELP

Answers

Answer:

a. w<1

Step-by-step explanation:

divide by -11 from both sides, when you divide by a negative number, flip the sign

What is the equation of this line?


Answers

Answer:

A

Step-by-step explanation:

plz brainliest :)

do you want an explanation?

A

Explanation : your welcome

PLEASEEE HELP!!!!!!!!!!

Answers

Okay ill help but tell me the answer first.

solve the equation 24 = y + 19
y=

Answers

Answer: y = 6/5

Step-by-step explanation:

what mixed numbers divide to 12

Answers

The mix numbers that divide to 12 are

12•1
24•2
36•3
72•6
60•5
84•7
48•4
Yes these all equal 12

work out( 10-3 times 2)^2

Answers

Answer:

16

Step-by-step explanation:

The answer is 16

Gabrielle read 53 pages of her book in the morning,
She read 26 fewer pages in the afternoon"
How many pages did Gabrielle read in the afternoon?
Solve on paper. Then, check your work on Zearn. )
Gabrielle read 1 pages in the afternoon. 1)

Answers

Answer:

27 pages

Step-by-step explanation:

This is a subtraction problem

26 fewer so you subtract 26

53 - 26 = 27

If r(x) = 2x^2 – 5x + 1, find r(x + 2)

Answers

Step-by-step explanation:

1 Expand by distributing terms.

rx+r×2

2 Regroup terms.

rx+2r

Find the Shaded Area:
10 m
10 m

Answers

Answer:

100-25pi m

Step-by-step explanation:

Let us subtract the circles area from the square

First, let us find the area of the square:

Base x height =

10m x 10m = 100m

Now, the circle:

pi x radius ^2 =

pi x (10/2)^2 =

pi x 5^2=

25 pi

Therefore, the shaded area is 100-25pi m. You can also simplify it further by plugging in the 3.14... value into pi.

I hope this helps! :)

Divide £48 in the following ratios.
a 2:1 b) 1:3

Answers

Answer:

a) £32 and £16

b) £12 and £36

Step-by-step explanation:

It is given that:

Amount to divide = £ 48

a) 2 : 1

Let,

x be the times of share.

2x + x = 48

3x = 48

Dividing both sides by 3

[tex]\frac{3x}{3}=\frac{48}{3}\\x=16[/tex]

Thus,

2x = 2(16) = £32

x = £16

b) 1 : 3

x+3x=48

4x=48

Dividing both sides by 4

[tex]\frac{4x}{4}=\frac{48}{4}\\x=12[/tex]

x = £12

3x = 3(12) = £36

Therefore,

a) £32 and £16

b) £12 and £36

Someone! I need help.

Answers

Answer:

With?

Step-by-step explanation:

During his lunch break, Leon sent 6 texts in 3/4

of a minute. What was his rate of texting?

Answers

Answer:

His rate was 8 text per minute... Please brainliest?

Answer: 8

Step-by-step explanation: trust me

URGENT!!!! THIS IS DUE TODAY!!

Answers

Answer:

Unless I am an idiot here (think I am) it is AE s the length between A and E, so it is 8

Step-by-step explanation:

Every side of the square is 16.

A to E is half of a side of the square, not a full side.

So you divide 16 by 2, getting 8.

Hope this helps, and sorry if this seems sloppy, I am new to brainly :)

Find the sum.
(3x - 4) + (12x + 10)​

Answers

Answer:

15x+6

Step-by-step explanation:

Answer:

hiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii

What is the domain and range of the inverse of: f (x)= (x + 2)² - 1

Answers

Answer:

The inverse of this function is a parabola that has been rotated 90 degrees clockwise, with it's vertex at point 1, 0.

So it's domain is x ≥ 1

And it's range is y ≥ -2

Step-by-step explanation:

Given:

f(x) = (x + 2)² - 1

First we find the inverse:

x = (f(x) + 2)² - 1

x - 1 = (f(x) + 2)²

√(x - 1) = f(x) + 2

f(x) =  -2 ± √(x - 1)

If 2000 is placed into a bank account that pays 3% compond interest per year, how much will be in the account after 2 years

Answers

Answer:

Interest =(Principle ×Rate×Time)/100

=(2000×3×2)/100

=$120

Total money in the account=$120+$2000

=$2120

Step-by-step explanation:

WHICH STAMENT IS TRUE ABOUT THE GRAPH SHOWN

Answers

I think its A but im not sure

A school band is buying new jackets and hats. A jacket costs $100 and a hat costs $40. The expression 100/+40h represents the cost of /jackets and h hats. How much will 5 new jackets and 8 new hats cost?​

Answers

Answer:

820

Step-by-step explanation:

100j+40h

100(5)+40(8)

500+320

820!

Calculate the perimeter of the shape to the nearest whole number

Answers

Answer:

Option B

Step-by-step explanation:

Perimeter of the given figure = Sum of measures of all sides

                                                = AB + BC + CA

Since, AB = BC = 9 cm (Radii)

CA = Length of arc CA which is the quarter of the circumference of a circle with radius 9 cm

CA = [tex]\frac{1}{4}(\text{Circumference of the circle})[/tex]

      = [tex]\frac{1}{4}(2\pi r)[/tex]

      = [tex]\frac{1}{2}(\pi )(9)[/tex]

      = 14.14 cm

Now perimeter of the shape = 9 + 9 + 14.14

                                                = 32.14 cm

                                                ≈ 32 cm

Therefore, Option B will be the correct option.

Need a bit of help here. :/

Answers

Answer:

A or B

Step-by-step explanation:

Which is the corresponding angle

Answers

Answer:

4 and 8

Step-by-step explanation:

4 and 8 are corresponding angles as they form at parallel lines cut by a transversal.

4 and 3 are supplementary angles (they both add up to 180°).

4 and 1 are vertically opposite angles and are equal to each other.

From the above explanations, only 4 and 8 are corresponding angles.

I hope this helps! I would really appreciate it if you would please mark me brainliest! Have a blessed day!

How do i solve this??

Answers

Answer:

x = 25

Step-by-step explanation:

It's a square, so:

[tex]4(4x-10)=360\\16x-40=360\\16x=400\\x=25[/tex]

Other Questions
Which of the following is NOT a characteristic of the Berbers? *native to Africafarmersherded cattlethey did not take part in the Trans-Saharan Trade ( look at photo) y=12x+ GRAPH PLEASE HELP OR BRIANLIEST GET RIGHT Jace has to read 40 pages in his novel tonight. He has only read 8 pages so far. What percent of the pages has he read? 1. What is the criteria necessary for organisms to be classified in the same species? (Choose all that apply)A: offspring produced must look identical to the parentsB: must be capable of surviving in the same environmental conditionsC: offspring produced must be fertileD: must be capable of interbreeding with one another according to the kinetic theory the pressure exerted by a sample of gas at constant volume doubles when the absolute temperature is doubled because what do i do to get the answer i will give brainliest to first person. Please help with all of the questions The treaty of Paris gave Great Britain______ How might the steps of the Eightfold Path help Buddhists overcome selfish desires? PLEEEASEE HELPPP I WILL GIVE BRAINLIESTTTT!!!!!!!!!!! 40 POINTS!!! Maria invests 4500 in a savings account for 3 years the account pays simple interest at a rate of 1.8% per year work out the annual rate of simple interest 2 is a root of x 9x+ + 24x2 16 = ( two times.Please select the best answer from the choices providedO F Which kind of bond is formed when two atoms share electorons to form a molecule What is the name of this molecular compound> F6I5 pleasee and thank youuuu! Which of the following makes Iran a theocracy?A: Iranians elect their president .B: Iranians elect their parliament.C: its government is controlled by ayatollah.D: the government encourages science education. 6 examples of fiction and non fiction if 12 +0= 1 + 12, then ___ must equal: i need help over here also, the second question is Describe the process you used to solve the equation Why did missionaries stay in Hawaii? please answer this question