Show am example of a rational number that is between square root of 10 and square root of 11.
A. 16/5
B. 3.1
C. 3.4
D. 10/3
To determine which option is a rational number between the square root of 10 and the square root of 11, we can estimate the decimal values of the square roots:
√10 ≈ 3.162
√11 ≈ 3.317
Now we can identify the rational number from the options provided:
A. 16/5 ≈ 3.2
B. 3.1 (or 31/10) is less than √10.
C. 3.4 is greater than √11.
D. 10/3 (or 3.333...) is less than √11.
Among the options, only A, 16/5, falls within the range between the square root of 10 and the square root of 11.
Therefore, the answer is A. 16/5.
What is the least integer whose square root is an irrational number between 5 and 7?
A. 6
B. 25
C. 26
D. 13
To find the least integer whose square root is an irrational number between 5 and 7, we need to identify the perfect squares that are closest to 5 and 7:
√5 ≈ 2.236
√7 ≈ 2.646
Now, we can examine the options provided:
A. The square root of 6 is approximately 2.449 (irrational).
B. The square root of 25 is 5 (rational).
C. The square root of 26 is approximately 5.1 (irrational).
D. The square root of 13 is approximately 3.606 (irrational).
Among the options, the least integer whose square root is an irrational number between 5 and 7 is 26.
Therefore, the answer is C. 26.
Which irrational number is between square root of 14 and square root of 18?
A. Square root of 13
B. Square root of 10
C. Square root of 15
D. Square root of 19
To determine which irrational number is between the square root of 14 and the square root of 18, we can estimate the decimal values of these square roots:
√14 ≈ 3.742
√18 ≈ 4.243
Now we can identify the irrational number from the options provided:
A. The square root of 13 is approximately 3.606 (less than √14).
B. The square root of 10 is approximately 3.162 (less than √14).
C. The square root of 15 is approximately 3.873 (between √14 and √18).
D. The square root of 19 is approximately 4.359 (greater than √18).
Among the options, only C, the square root of 15, falls within the range between the square root of 14 and the square root of 18.
Therefore, the answer is C. Square root of 15.
How many Irrational numbers are there between square root of 11 and 17?
A. twenty eight numbers
B. Six numbers
C. Four numbers
D. An infinite number
To determine the number of irrational numbers between the square root of 11 and 17, we need to consider the interval between these two values.
√11 ≈ 3.317
√17 ≈ 4.123
Since √11 is approximately 3.317 and √17 is approximately 4.123, we can conclude that there is an infinite number of irrational numbers between these two values.
Thus, the answer is D. An infinite number.