Make a table of decimal numbers whose squares are close to 8.
A
3
B
2.8
Practice makes perfect
We are asked to approximate sqrt(8) 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 squares are close to 8.
Number
Square of Number
1
1^2=1
2
2^2= 4
3
3^2= 9
4
4^2=16
Our table shows that 8 is between the perfect squares 4 and 9. Because 8 is closer to 9 than to 4, we can say that sqrt(8) is closer to sqrt(9) than to sqrt(4). This means that sqrt(8) is closer to 3 than to 2.
We have that sqrt(8) is approximately 3.
Now we want to approximate sqrt(8) to the nearest tenth. We will make a table of decimal numbers between 3 and 2 whose squares are close to 8.
Number
Square of Number
2.6
2.6^2=6.76
2.7
2.7^2=7.29
2.8
2.8^2= 7.84
2.9
2.9^2= 8.41
The table shows that 8 is between 7.84 and 8.41. Because 8 is closer to 7.84 than to 8.41, we can say that sqrt(8) is closer to sqrt(7.84) than to sqrt(8.41). This means that sqrt(8) is closer to 2.8 than to 2.9.
