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
sukhopar [10]
3 years ago
7

A rational number raised to a rational power can either be rational or irrational. For example, 4^( 1/ 2) is rational because 4

^1 /2 = 2, and 2^ 1 /4 is irrational because 2^ 1/ 4 = √2/ 4 .
In this problem, you will investigate the possibilities for an irrational number raised to an irrational powerCan the value of an irrational number raised to an irrational power ever be rational?
Mathematics
1 answer:
Lady bird [3.3K]3 years ago
7 0

Answer:

Step-bThis is an interesting problem. To solve it I should find two irrational numbers r and s such that rs is rational.

I am not sure I am able to do that. However, I am confident that the following argument does solve the problem.

As we know, √2 is irrational. In particular, √2 is real and also positive. Then √2√2 is also real. Which means that it is either rational or irrational.

If it's rational, the problem is solved with r = √2 and s = √2.

Assume √2√2 is irrational. Let r = √2√2 and s = √2. Then rs = (√2√2)√2 = √2√22 = √22 = 2. Which is clearly rational.

Either way, we have a pair of irrational numbers r and s such that rs is rational. Or do we? If we do, which is that?

(There's an interesting related problem.)

Chris Reineke came up with an additional example. This one is more direct and constructive. Both log(4) and √10 are irrational. However

√10 log(4) = 10log(2) = 2.y-step explanation:

You might be interested in
Jan's average score after fifteen tests was 82. Her average on the next five tests was 90. What was her average score for all tw
Leokris [45]

Answer:

86

Step-by-step explanation:

82+90=172

172/2 (divided by two because thats how many numbers we added up to get 172)

172/2=86

86 is your answer

4 0
3 years ago
Hexagon FUTBOL has coordinates F(3,6), U(5,2), T(2,-3), B(-3,-2), O(-5,1) and L(-2,5), and it is dilated by scale factor of five
Arturiano [62]
It’s B (-3,-2) thats the andwer
7 0
3 years ago
Read 2 more answers
Simplify: <br>5√3+4√12-2√75​
svlad2 [7]

Answer:

8 + 5\sqrt{3}-10\sqrt{7}

Step-by-step explanation:

i just wrote 5\sqrt{3} as a decimal

times 2 with 4\sqrt{1} and

times 5 with -2\sqrt{7}

i might be wrong but hope this helps

3 0
3 years ago
What's the answer I need he
LiRa [457]
Divide 425/14 which gives us 30.35. . .

It says about so we'll round it $30 per day.
6 0
3 years ago
Read 2 more answers
What is the approximate rate of change in the total calories Leo burned between 40 and 70 minutes?
Contact [7]

Answer:

Is that the second part of the question? Cuz dat dont make no sense

Im Leo lm.ao

8 0
3 years ago
Other questions:
  • HELP ASAP PLEASE!!!!
    14·1 answer
  • Simplify the expression.
    12·2 answers
  • PLEASE HELP ASAP! A mountain climber is at an altitude of 2.9 mi above the earth’s surface.
    5·1 answer
  • 3 thousand ÷10 standard form
    15·2 answers
  • Prove that 3(x+1)(x+7)-2x+5)^2 is never positive
    6·1 answer
  • PLEASE HELP ME!!! Which expression is equivelent to 4(9+7) A. 36 + 7 B. 13 + 11 C. 36 + 28 D. 13 + 7
    7·2 answers
  • 6x-2&lt;4x+12 solve the inequality
    13·2 answers
  • During a sale, every item in a store is 80% of its regular price. If the regular price of a T-shirt is $10, what is its sale pri
    8·1 answer
  • Solve the following equation simultaneously 2a-3b+10=0, 10a+6b=8​
    11·1 answer
  • Please help quickly it is due in 46 minutes
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!