Which irrational number is between 14√ and 18√?
To find an irrational number between 14√ and 18√, we need to identify a perfect square between these two numbers.
To do this, we can square some numbers between 14 and 18 and compare the result to the numbers in question.
When we square 14, we get 196, and when we square 15, we get 225.
Therefore, 14² < 14√² = 196 < 225 = 15² < 18√².
Therefore, we can conclude that an irrational number between 14√ and 18√ is √196, which equals 14.
Which irrational number is between 14√ and 18√?
Responses
19√
15√
13√
10√
To find an irrational number between 14√ and 18√, we can calculate the decimal approximation of both numbers and identify a number that lies between them.
Approximating 14√ and 18√:
14√ ≈ 14 × 1.414 = 19.796
18√ ≈ 18 × 1.414 = 25.452
Based on these approximations, we can see that the irrational number between 14√ and 18√ is approximately between 19.796 and 25.452.
Out of the given options, the only number that fits this range is 19√.
Show an example of a rational number that is between 10−−√ and 11−−√.
To find a rational number between √10 and √11, we can take the average of these two irrational numbers.
√10 ≈ 3.162
√11 ≈ 3.317
The average of √10 and √11 is (3.162 + 3.317) / 2 ≈ 3.24.
Therefore, a rational number between √10 and √11 is 3.24.
How many irrational numbers are there between 11√ and 17√?
Responses
twenty-eight numbers
four numbers
an infinite number
six numbers
To determine how many irrational numbers are between 11√ and 17√, we need to consider that irrational numbers are infinite and dense within the real number line.
Since the square root of any positive number gives an irrational result, we can establish that there are infinitely many irrational numbers between 11√ and 17√.
Therefore, the correct response is "an infinite number" of irrational numbers.