Make a table of decimal numbers whose cubes are close to 12.
A
- 2
B
- 2.3
Practice makes perfect
We are asked to approximate sqrt(- 12) 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 cubes are close to 12.
Number
Square of Number
1
1^3= 1
2
2^3= 8
3
3^3= 27
4
4^3= 64
Our table shows that 12 is between the perfect cubes 8 and 27. Because 12 is closer to 8 than to 27, we can say that sqrt(12) is closer to sqrt(8) than to sqrt(27). This means that sqrt(12) is closer to 2 than to 3.
We have that sqrt(12) is approximately 2. If we bring back the negative sign, we can say that sqrt(- 12) is approximately - 2.
Now we want to approximate sqrt(- 12) to the nearest tenth. Once again, we will ignore the negative sign for a while. We will make a table of decimal numbers between 2 and 3 whose squares are close to 12.
Number
Square of Number
2.1
2.1^3=9.3
2.2
2.2^3= 10.6
2.3
2.3^3= 12.2
2.4
2.4^3=13.8
The table shows that 12 is between 10.6 and 12.2. Because 12 is closer to 12.2 than to 10.6, we can say that sqrt(12) is closer to sqrt(12.2) than to sqrt(10.6). This means that sqrt(12) is closer to 2.3 than to 2.2.
We have that sqrt(12) is approximately 2.3. If we bring back the negative sign, we can say that sqrt(- 12) is approximately - 2.3.
