1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
otez555 [7]
2 years ago
6

Express (8 - 3sqrt(2))/(4 + 3sqrt(2)) in the form of a + b * sqrt(2) where a and b are integers.​

Mathematics
1 answer:
Naya [18.7K]2 years ago
3 0

Answer:   \boldsymbol{-25+18\sqrt{2}}

The expression is in the form a+b\sqrt{2} where a = -25 and b = 18

==========================================================

Work Shown:

Let x = 3\sqrt{2} and then square both sides

x = 3\sqrt{2}\\\\x^2 = \left(3\sqrt{2}\right)^2\\\\x^2 = \left(3\right)^2*\left(\sqrt{2}\right)^2\\\\x^2 = 9*2\\\\x^2 = 18\\\\

We'll use both x and x^2 later on.

---------------------

The denominator is in the form 4+x. We'll multiply top and bottom by 4-x to then use the difference of squares rule. This will allow us to eliminate the square root in the denominator.

\frac{8-3\sqrt{2}}{4+3\sqrt{2}}\\\\\frac{8-x}{4+x}\\\\\frac{(8-x)(4-x)}{(4+x)(4-x)}\\\\\frac{32-8x-4x+x^2}{16-x^2} \ \text{ difference of squares rule}\\\\\frac{32-12x+x^2}{16-x^2}\\\\

\frac{32-12*3\sqrt{2}+18}{16-18} \ \text{ plug in } x = 3\sqrt{2} \text{ and } x^2 = 18\\\\\frac{50-36\sqrt{2}}{-2}\\\\\frac{-2(-25+18\sqrt{2})}{-2}\\\\\boldsymbol{-25+18\sqrt{2}}

Therefore,

\frac{8-3\sqrt{2}}{4+3\sqrt{2}}=\boldsymbol{-25+18\sqrt{2}}

-------------------------------------

Checking the answer:

Use a calculator to find that,

\frac{8-3\sqrt{2}}{4+3\sqrt{2}} \approx 0.45584412271571 \\\\-25+18\sqrt{2} \approx 0.45584412271571

We get the same decimal approximation, which helps confirm the correct answer.

Or you could use the idea that if M = N, then M-N = 0 to subtract the original expression M and the final result N. You should get 0 or very close to it.

You might be interested in
Please help me is due today and I am being timed
ivanzaharov [21]

Answer:

B

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
I have a water tank that holds 5 gallons of water I drink 4 pints of water a day how many full tanks of water I will be drinking
julsineya [31]


                             gfdddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddd

4 0
2 years ago
Find the greatest common factor of the following monomials: 20a 46a^2 48a^6​
Ierofanga [76]
60a^5 is the answer to your question
6 0
2 years ago
.
Tatiana [17]
Multiply original price by 90%
8 0
2 years ago
Read 2 more answers
Find the domain and range of the relation.<br> {(3,-2) (2,1) (-1,0) (1,3)}
svp [43]
The domain of the inverse of a relation is the same as the range of the original relation. In other words, the y-values of the relation are the x-values of the inverse.
5 0
2 years ago
Other questions:
  • Function P represents the number of people in the library on a Monday as a function of hours since the library opened
    9·1 answer
  • Can anybody help me out ?
    15·1 answer
  • A publishing company is going to have 24,000 books printed. There are between 3 and 4 books out of ever 3,000 that will have a p
    13·1 answer
  • Solve the system of equations,
    12·1 answer
  • The dimensions of a rectangular prism are 24 ft x 20 ft x 15 ft. What is the surface area
    5·1 answer
  • Solve the following system of linear equations by using the Elimination Method:
    9·1 answer
  • Fatima told her grand children if i give 2 toffees each of you i am left with 3 toffees.But if i try to give 3 toffees each of y
    9·1 answer
  • Which points are reflections of each other across the y-axis?
    12·1 answer
  • A delivery company charges a flat rate of $3 for a large envelope plus an additional $0.25 per ounce for every ounce over a poun
    12·1 answer
  • Two lines intersect at a point, forming angle 1, angle 2, angle 3, and angle 4.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!