Make a table of decimal numbers whose squares are close to 24.
A
- 5
B
- 4.9
Practice makes perfect
We are asked to approximate - sqrt(24) to the nearest integer. This number must be approximated rather than evaluated because it is an irrational number.
Irrational Number
A number that cannot be written as ab, where a and b are integers and b is not zero.
To do this approximation, we will need to ignore the negative sign for now. Let's start by making a table of numbers whose squares are close to 24.
Number
Square of Number
2
2^2=4
3
3^2=9
4
4^2= 16
5
5^2= 25
Our table shows that 24 is between the perfect squares 16 and 25. Because 24 is closer to 25 than to 16, we can say that sqrt(24) is closer to sqrt(25) than to sqrt(16). This means that sqrt(24) is closer to 5 than to 4.
Therefore, we have that sqrt(24) is approximately 5. If we bring back the negative sign, we can say that - sqrt(24) is approximately - 5.
Now we want to approximate - sqrt(24) to the nearest tenth. Once again, we will ignore the negative sign for a while. We will make a table of decimal numbers between 4 and 5 whose squares are close to 24.
Number
Square of Number
4.6
4.6^2=21.16
4.7
4.7^2=22.09
4.8
4.8^2= 23.04
4.9
4.9^2= 24.01
The table shows that 24 is between 23.04 and 24.01. Because 24 is closer to 24.01 than to 23.04, we can say that sqrt(24) is closer to sqrt(24.01) than to sqrt(23.04). This means that sqrt(24) is closer to 4.9 than to 4.8.
Therefore, we have that sqrt(24) is approximately 4.9. If we bring back the negative sign, we can say that - sqrt(24) is approximately - 4.9.
