Make a table of decimal numbers whose cubes are close to 60.
A
4
B
3.9
Practice makes perfect
We are asked to approximate sqrt(60) 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.
Let's start by making a table of numbers whose cubes are close to 60.
Number
Square of Number
1
1^3=1
2
2^3=8
3
3^3= 27
4
4^3= 64
Our table shows that 60 is between the perfect cubes 27 and 64. Because 60 is closer to 64 than to 27, we can say that sqrt(60) is closer to sqrt(64) than to sqrt(27). This means that sqrt(60) is closer to 4 than to 3.
Therefore, we have that sqrt(60) is approximately 4.
Now we want to approximate sqrt(60) to the nearest tenth. We will make a table of decimal numbers between 3 and 4 whose cubes are close to 60.
Number
Square of Number
3.8
3.8^3=54.8
3.9
3.9^3= 59.3
4
4^3= 64
4.1
4.1^3=68.9
The table shows that 60 is between 59.3 and 64. Because 60 is closer to 59.3 than to 64, we can say that sqrt(60) is closer to sqrt(59.3) than to sqrt(68.9). This means that sqrt(60) is closer to 3.9 than to 4.
Therefore, we have that sqrt(60) is approximately 3.9.
