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
Lostsunrise [7]
3 years ago
14

How do you simplify

20%5Csqrt%7B6%7D%20%20%7D" id="TexFormula1" title="\frac{\sqrt{2} +\sqrt{6} }{\sqrt{8} + \sqrt{6} }" alt="\frac{\sqrt{2} +\sqrt{6} }{\sqrt{8} + \sqrt{6} }" align="absmiddle" class="latex-formula">?
Mathematics
1 answer:
blondinia [14]3 years ago
7 0

The trick is to exploit the difference of squares formula,

a^2-b^2=(a-b)(a+b)

Set a = √8 and b = √6, so that a + b is the expression in the denominator. Multiply by its conjugate a - b:

(\sqrt8+\sqrt6)(\sqrt8-\sqrt6)=(\sqrt8)^2-(\sqrt6)^2=8-6=2

Whatever you do to the denominator, you have to do to the numerator too. So

\dfrac{\sqrt2+\sqrt6}{\sqrt8+\sqrt6}=\dfrac{(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)}{(\sqrt8+\sqrt6)(\sqrt8-\sqrt6)}=\dfrac{(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)}2

Expand the numerator:

(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=\sqrt{2\cdot8}+\sqrt{6\cdot8}-\sqrt{2\cdot6}-(\sqrt6)^2

(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=\sqrt{16}+\sqrt{48}-\sqrt{12}-6

(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=4+\sqrt{48}-\sqrt{12}-6

(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=-2+\sqrt{12}(\sqrt4-1)

(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=-2+\sqrt{12}(2-1)

(\sqrt2+\sqrt6)(\sqrt8-\sqrt6}=-2-\sqrt{12}

So we have

\dfrac{\sqrt2+\sqrt6}{\sqrt8+\sqrt6}=-\dfrac{2+\sqrt{12}}2

But √12 = √(3•4) = 2√3, so

\dfrac{\sqrt2+\sqrt6}{\sqrt8+\sqrt6}=-\dfrac{2+2\sqrt3}2=\boxed{-1-\sqrt3}

You might be interested in
supervisor records the repair cost for 25 randomly selected dryers. A sample mean of $93.36 and standard deviation of $19.95 are
Simora [160]
<h2><u>Answer with explanation:</u></h2>

The confidence interval for population mean (when population standard deviation is unknown) is given by :-

\overline{x}-t^*\dfrac{s}{\sqrt{n}}< \mu

, where n= sample size

\overline{x} = Sample mean

s= sample size

t* = Critical value.

Given : n= 25

Degree of freedom : df=n-1=24

\overline{x}= \$93.36

s=\ $19.95

Significance level for 98% confidence interval : \alpha=1-0.98=0.02

Using t-distribution table ,

Two-tailed critical value for 98% confidence interval :

t^*=t_{\alpha/2,\ df}=t_{0.01,\ 24}=2.4922

⇒ The critical value that should be used in constructing the confidence interval = 2.4922

Then, the 95% confidence interval would be :-

93.36-(2.4922)\dfrac{19.95}{\sqrt{25}}< \mu

=93.36-9.943878< \mu

=93.36-9.943878< \mu

=83.416122< \mu

Hence, the 98% confidence interval for the mean repair cost for the dryers. = 83.4161

4 0
3 years ago
How do organism replace dead or injured cells? Organisms can take cells from other organisms. Organisms are limited to the amoun
Gnoma [55]

Answer: Organisms go through mitosis that allows new identical cells to be made.

explanation:

mitosis also occures when cells are worn out or are injured and the mitosis will replace the injured cells

8 0
3 years ago
Please Help Me I Need Finish This Tonight
vladimir2022 [97]
1) a- rectangle
    b- same place you started, facing west
2) a- right triangle
    b- parallelogram
    c- not sure the specific name they are looking for...
    * also have no clue what a recipe is in terms of this lol
3) a- square
    b- rectangle, depending on the length of the segments and their distance  
    apart
4) not sure

5 0
3 years ago
I am stuck on these two, please help if you can. thank you :)
Sever21 [200]

Answer:

23) x= \frac{27}{8}

24) x= 8\sqrt{3}

Step-by-step explanation:

3 0
3 years ago
Which equation is equivalent to
Paul [167]

Answer:

c) 3x - 45 = 10

Step-by-step explanation:

\frac{1}{5}x-3=\frac{2}{3}\\\\\frac{1}{5}x-\frac{3*5}{1*5}=\frac{2}{3}\\\\\frac{x-15}{5}=\frac{2}{3}\\

Cross multiply,

3*(x - 15) = 2*5

3*x - 3*15 = 10

3x - 45 = 10

4 0
3 years ago
Other questions:
  • A light bulb consumes 3120 watt-hours in 3 days and 6 hours. How many watt-hours does it consume per day?
    14·1 answer
  • Find the degree of the polynomial <br> 5mn^4+7mn^2p^5+15np
    5·2 answers
  • Martin has 4 pizzas, and he wants to cut them all into 1/8’s. How many pieces will Martin have?
    10·1 answer
  • A khanacademy.org Differential equations: exponential model word problems You might need: Calculator A controversial story comes
    13·1 answer
  • Four equals the difference of eight and a number and the result is divided by four
    15·1 answer
  • Can someone help me plslsssssss
    11·1 answer
  • 23.5 + - (-62.74) = ​
    5·2 answers
  • Can i have some help
    9·1 answer
  • Chicken costs $3.40 per pound and beef costs $4.30 per pound What is the cost of 3 pounds of chicken? What is the cost of 3 poun
    9·2 answers
  • Here are the first four terms of an arithmetic sequence. 3,10,17,24. Is 150 a term in this sequence?
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!