why is 9/4 close to the square root of 5
9/4 is not close to the square root of 5. The square root of 5 is approximately 2.236. The fraction 9/4 is equal to 2.25, which is close to the square root of 5, but not exactly the same.
To determine why 9/4 is close to the square root of 5, we can use approximation.
First, let's calculate the square root of 5. The square root of 5 is approximately 2.2360679775.
Now, let's simplify 9/4. Dividing 9 by 4 gives us 2.25.
Comparing the two values, we can see that 2.25 is very close to 2.2360679775.
Therefore, 9/4 is close to the square root of 5 when approximated.
To understand why 9/4 (or 2.25) is close to the square root of 5, we can take a closer look at the calculations involved:
1. Square root of 5 (√5): The square root of a number is the value that, when multiplied by itself, gives the original number. In the case of 5, its square root is an irrational number, approximately 2.236.
2. 9/4 (or 2.25): When dividing 9 by 4, we get a decimal representation of 2.25.
So, while 9/4 is not exactly equal to the square root of 5, it is close. The reason for this closeness is that 2.25 is an approximation of the irrational number √5.
If you want to calculate the square root of 5 more precisely, you can use a calculator or a programming language that supports square root functions.