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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:

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barxatty [35]

Answer:

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6 0
3 years ago
scott can reach 57 inches high. scott stands on box that is 16 inches high how many inches high can scott reach now?
kompoz [17]

Answer: 73 inches high

Step-by-step explanation: 57+16=73

4 0
3 years ago
What is the smallest Square number using 5 roman numerals?
In-s [12.5K]

Answer:

The answer is "1"

Step-by-step explanation:

Let 5 roman numbers are:

\to I=1\\\\\to II=2\\\\\to III=3\\\\\to IV= 4\\\\\to V=5

There square values are as follows:

\to 1^2=1\\\\\to 2^2=4\\\\\to 3^2=6\\\\\to 4^2=16\\\\\to 5^2=25

The smallest square number is= 1.

3 0
3 years ago
The charge for a bicylce repair was $9.28 for parts, 1/4 hour of labor at $18 per hour, and a $2 shop fee. What was the total co
Bas_tet [7]
9.28 plus 2 is 11.28. 1/4 of 18 is 4.50. Add 4.50 to 9.28 and your total is $15.78.

The equation would be:
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3 years ago
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Sati [7]

Answer:

$20

Step-by-step explanation:

I = 400(.05)(1)

I = 20

3 0
2 years ago
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