Which irrational number is between 14−−√ and 18−−√?
To find an irrational number between $\sqrt{14}$ and $\sqrt{18}$, we consider the average of these two numbers: $\frac{\sqrt{14}+\sqrt{18}}{2}$. Since $\sqrt{14}$ and $\sqrt{18}$ are both irrational, $\frac{\sqrt{14}+\sqrt{18}}{2}$ is also irrational. Thus, an irrational number between $\sqrt{14}$ and $\sqrt{18}$ is $\boxed{\frac{\sqrt{14}+\sqrt{18}}{2}}$.
Which irrational number is between 14−−√ and 18−−√?
To find an irrational number between √14 and √18, we can determine the average of these two numbers.
Let's calculate:
√14 ≈ 3.74
√18 ≈ 4.24
The average of these two numbers is (3.74 + 4.24) / 2 = 8.98 / 2 = 4.49.
Therefore, the irrational number between √14 and √18 is approximately 4.49.
To find an irrational number between √14 and √18, we can start by approximating the values of these square roots.
√14 is between 3 and 4, because 3 squared is 9 and 4 squared is 16. So, we have:
3 < √14 < 4
Similarly, √18 is between 4 and 5, because 4 squared is 16 and 5 squared is 25. So, we have:
4 < √18 < 5
Now, let's find an irrational number between these two approximations.
One well-known irrational number is √2, which is approximately 1.41421356. Since √14 is between 3 and 4, we can multiply the approximation of √2 by 3, resulting in approximately 4.24264068.
So, we can conclude:
√2 * 3 ≈ 4.24264068
Therefore, an irrational number between √14 and √18 is approximately 4.24264068.