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
please calculate the volume of the cylinder below. use 3.14 as approximation for Pi. (MIDDLE SCHOOL MATH)​
Gnom [1K]

the answer is V≈254.47

3 0
3 years ago
Please Help!!! I need help
Firlakuza [10]

Answer:

I cant see anything

Step-by-step explanation:

SRY U_U

6 0
3 years ago
Complete the derivation of the formula for a cylinder
viva [34]

Answer:

2r(2r)

R

Pi/4

Pi times r cubed

Step-by-step explanation:

Believe it or leave it

4 0
3 years ago
Evaluate the expression.<br> 23.6 - 2x3° divides by 2
Grace [21]
43 is thee answererrr
5 0
3 years ago
Given the following inverse variation find the missing value: (5,-8) (20, y) find the missing value
forsale [732]
This answer is pretty simple. you see (5,-8) and (20,y). well the 20 is 4 times the 5 on the x value so multiply the y value by 4 to get your answer which Y=-32 in the 2nd corrdenants.
6 0
3 years ago
Other questions:
  • The graphed line can be expressed by which equation?
    13·2 answers
  • What combination of transformations is shown below
    11·2 answers
  • NEED HELP ASAP SHOW WORK AND PLZ EXPLAIN
    7·1 answer
  • Please help!
    6·1 answer
  • For the linear equation y = -2x - 4, find the missing coordinate (3, ____)
    9·1 answer
  • Select the correct answer.<br> Which statement is true?
    9·1 answer
  • A light bulb consumes 9900 watt-hours in 5 days and 12 hours. How many watt-hours does it consume per day?
    12·1 answer
  • 1ll mark brainlist pleassee help
    10·1 answer
  • I really need this answer ASAP! Please answer correctly! No links please.
    10·1 answer
  • The sum of two consecutive integers is 75.<br> What is the first number?
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!