Make a table of decimal numbers whose squares are close to 14.
A
4
B
3.7
Practice makes perfect
We want to approximate sqrt(14) 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 make a table of numbers whose squares are close to 14.
Number
Square of Number
2
2^2=4
3
3^2= 9
4
4^2= 16
5
5^2=25
Our table shows that 14 is between the perfect squares 9 and 16. Because 14 is closer to 16 than to 9, we can say that sqrt(14) is closer to sqrt(16) than to sqrt(9). This means that sqrt(14) is closer to 4 than to 3.
Therefore, we know that sqrt(14) is approximately 4.
Now we want to approximate sqrt(14) to the nearest tenth. We will make a table of decimal numbers between 3 and 4 whose squares are close to 14.
Number
Square of Number
3.6
3.6^2=12.96
3.7
3.7^2= 13.69
3.8
3.8^2= 14.44
3.9
3.9^2=15.21
The table shows that 14 is between 13.69 and 14.44. Because 14 is closer to 13.69 than to 14.44, we can say that sqrt(14) is closer to sqrt(13.69) than to sqrt(14.44). This means that sqrt(14) is closer to 3.7 than to 3.8.
Therefore, we know that sqrt(14) is approximately 3.7.
