To find a rational number and an irrational number between $6-\sqrt{2}$ and $8-\sqrt{2}$, we can first figure out the size of the gap between the two numbers. The difference between $6-\sqrt{2}$ and $8-\sqrt{2}$ is $(8-\sqrt{2}) - (6-\sqrt{2}) = 8-6 = 2.$ So, we need to find a rational and an irrational number that add up to 2.
To find the irrational number, we can choose a decimal number that is not rational. We can see that $6.33$ is a rational number since it terminates. So, it is not the irrational number.
Next, we look for an irrational number. Out of the given choices, we can see that $6.42$ has digits that go on forever without repeating.
Therefore, the answer is $\boxed{\text{(C)}\ 6.42}$.
Which of the following options includes a rational number and an irrational number between 6–√ and 8–√ ?(1 point) Choices: A. 6.17. B. 6.25 C. 6.42 D. 6.33
3 answers
Using a number line, what is the approximate value of 39−−√ ?(1 point) Choices: A. 6.17. B. 6.25 C. 6.42 D. 6.33
To find the approximate value of $39-\sqrt{2}$, we need to estimate where it falls on a number line.
First, remember that $\sqrt{2}$ is approximately equal to $1.41$. We can subtract $1.41$ from $39$ to get an estimate.
$39 - 1.41 \approx 37.59$
So, the approximate value of $39-\sqrt{2}$ is closest to $\boxed{\text{(A) } 37.59}$.
First, remember that $\sqrt{2}$ is approximately equal to $1.41$. We can subtract $1.41$ from $39$ to get an estimate.
$39 - 1.41 \approx 37.59$
So, the approximate value of $39-\sqrt{2}$ is closest to $\boxed{\text{(A) } 37.59}$.
1 answer