1. Rational numbers can be written as a ratio (fraction)
Whole numbers are rational. 5 = 5/1, for example.
Square roots are NOT rational. Example: √3
However, square roots of square numbers can be simplified, and are therefore rational. <span>√4 = 2, rational.</span>
√4 + <span>√16 = 2 + 4 = 6. rational
</span>√5 + √36...<span> irrational
</span>√9 + <span>√24... irrational
</span>2 × <span>√4 = 2 × 2 = 4. rational
</span>√49 × <span>√81 = 7 × 9 = 63. rational
</span>3√12... irrational
2.


3.


4.
![n^\frac1x=\sqrt[x]n](https://tex.z-dn.net/?f=n%5E%5Cfrac1x%3D%5Csqrt%5Bx%5Dn)
![\sqrt[3]{m^2n^5}=m^{\frac23}n^{\frac53}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bm%5E2n%5E5%7D%3Dm%5E%7B%5Cfrac23%7Dn%5E%7B%5Cfrac53%7D)
5.


A, since neither 3 nor 12 is a square but we end up with 6.
Pretty sure that the answer is B because if you plug in x+1 into 4x^2 you get 4(x+1)^2
Hi there
So, if the track is 1/8 of a mile, let's call every lap a "one-eighth mile" run. We know John ran 24 laps, or that he ran 24 "one-eighth miles," just consecutive, one right after another. Let's stop worrying about rates or tricks or math for a second, and just ask: how many real miles is 24 "one-eighth" miles? We know it's less than 24---a lot less, since you have to go around 8 times just to get to 1 mile. Well wait, if we go around 8 times, we get 1 mile. That means if we go around 28, or 16 times, we get 2 miles; And let's just think to the next full mile---if we go 38, or 24 times, we get 3 miles. He did go around 24 times, so he must have run 3 miles on a 1/8 track.
Division and multiplication are inverses of each other. So we solved this by looking for an intuition for how many full miles corresponded to how many laps, with a bunch of steps of multiplication. But you can cut right to the chase and solve it faster with division---24 laps * 1 mile per 8 laps, means:
total distance = 24 Lap (1 mi / 8 Lap) total distance = 24/8 total distance = 3
IF I want to rent the paddleboat I have to start with $10 and I have it for an hour it will be 18$. We are increasing by 8 for every hour we have the boat
c = 8h + 10