Which irrational number is between √14 and √18?
A. √13
B. √19
C. √15
D. √10
To determine which irrational number is between √14 and √18, we need to compare the values of these two numbers and the options provided.
√14 is approximately 3.74, and √18 is approximately 4.24.
√13 is approximately 3.61, which is less than √14.
√19 is approximately 4.36, which is greater than √18.
√15 is approximately 3.87, which lies between √14 and √18.
√10 is approximately 3.16, which is less than √14.
Therefore, the irrational number that is between √14 and √18 is √15.
The correct answer is C. √15.
How many irrational numbers are there between √11 and √17?
A. An infinite number
B. Four numbers
C. Twenty-eight numbers
D. Six numbers
To determine how many irrational numbers are between √11 and √17, we need to compare the values of these two numbers and consider the nature of irrational numbers.
√11 is approximately 3.32, and √17 is approximately 4.12.
Since irrational numbers cannot be expressed as a fraction or a terminating or repeating decimal, there are infinitely many irrational numbers between any two distinct real numbers.
Therefore, the correct answer is A. An infinite number.
To determine which irrational number is between √14 and √18, we need to calculate the approximate values of each square root.
Using a calculator, we find that √14 is approximately 3.74, and √18 is approximately 4.24.
Looking at the given options:
A. √13 is less than √14, so it cannot be the answer.
B. √19 is greater than √18, so it cannot be the answer.
C. √15 is between √14 and √18, so it is a possible answer.
D. √10 is less than √14, so it cannot be the answer.
Therefore, the correct answer is C. √15.