How many irrational number are there between √11 and √17?
To find the number of irrational numbers between √11 and √17, we need to determine the irrational numbers themselves and count how many there are.
We can start by writing out the square roots themselves:
√11 = 3.31662479...
√17 = 4.12310563...
These two numbers represent the approximate range between which the irrational numbers lie. However, there are infinitely many irrational numbers within this range. Therefore, we cannot determine an exact count of the number of irrational numbers.
In conclusion, the number of irrational numbers between √11 and √17 is infinite.
To determine the number of irrational numbers between √11 and √17, we need to find the irrational numbers within this range.
First, let's find the integer values for √11 and √17:
√11 ≈ 3.31662479
√17 ≈ 4.12310563
The integers within this range are 3 and 4. However, since we are looking for irrational numbers, we need to consider the numbers between these integers.
To find the irrational numbers, we can consider the square roots of the consecutive integers between 11 and 17 inclusively:
For 12: √12 ≈ 3.46410162 (irrational)
For 13: √13 ≈ 3.60555128 (irrational)
For 14: √14 ≈ 3.74165739 (irrational)
For 15: √15 ≈ 3.87298335 (irrational)
For 16: √16 ≈ 4 (rational)
Therefore, there are four irrational numbers between √11 and √17.