I got this picture from photomath, hope it helps
Answer:
68 cm
Step-by-step explanation:
√289 = 17
each side is 17 cm
17 * 4 = 68 cm
Answer:
I was asleep in bed one night when, suddenly, a loud noise woke me. I did not know what it was I searched around for a few minutes, but I couldn't find where the sound was coming from, but on the floor, I saw a broken wase, and i decided to throw it away in the open window next to me... My house was very far out, hidden behind trees, and darkness was around me. Ahhh! The sound was repeating again and again so I decided to rush over to my phone to call the police. but then I realized that was just not any sound, but it was a cry for help. The police said they will send over a rescue worker to help me, to help them, whoever it is. I went downstairs to find something sharp something that could help me or at least scare away the person here.
Step-by-step explanation:
Hope you like it xD It is not 100% finished so probably you can finish it, i wrote an introduction for you) good luck
A good place to start is to set 
to y. That would mean we are looking for 
to be an integer. Clearly, 
, because if y were greater the part under the radical would be a negative, making the radical an imaginary number, not an integer. Also note that since 
is a radical, it only outputs values from ![[0,\infty]](https://tex.z-dn.net/?f=%20%5B0%2C%5Cinfty%5D%20)
, which means y is on the closed interval: ![[0,120]](https://tex.z-dn.net/?f=%20%5B0%2C120%5D%20)
.
With that, we don't really have to consider y anymore, since we know the interval that is on.
Now, we don't even have to find the x values. Note that only 11 perfect squares lie on the interval , which means there are at most 11 numbers that x can be which make the radical an integer. All of the perfect squares are easily constructed. We can say that if k is an arbitrary integer between 0 and 11 then:
Which is strictly positive so we know for sure that all 11 numbers on the closed interval will yield a valid x that makes the radical an integer.
