How many irrational numbers are there between 11√ and 17√?
a four
b infinite
c twenty eight
d six
To determine the number of irrational numbers between 11√ and 17√, we first need to understand that irrational numbers are infinite and densely populated between any two integers.
Therefore, the answer is:
b) infinite
To find the number of irrational numbers between 11√ and 17√, we need to determine the number of square roots of integers between √11 and √17.
To do this, we can first simplify the square roots:
√11 ≈ 3.3166
√17 ≈ 4.1231
Now, we need to find the square roots of integers between 3.3166 and 4.1231. These square roots are irrational numbers.
To count the number of square roots, we can round down the value of √11 and round up the value of √17 to get the nearest whole numbers:
√11 ≈ 3
√17 ≈ 5
So, the number of square roots (and therefore the number of irrational numbers) between 11√ and 17√ is 5 - 3 = 2.
Therefore, the correct answer is d) six.
To determine how many irrational numbers are there between 11√ and 17√, we need to understand the nature of irrational numbers.
Irrational numbers are real numbers that cannot be expressed as fractions and have non-repeating, non-terminating decimal representations. Examples of irrational numbers include (√2, √3, π, etc.)
In this case, we have 11√ and 17√. The numbers between them are irrational numbers.
To find the number of irrational numbers between 11√ and 17√, we need to consider the density of irrational numbers. Since irrational numbers are infinitely dense, that means there are infinitely many irrational numbers between any two given irrational numbers.
Therefore, the correct answer is (b) infinite.