Make a table of decimal numbers whose squares are close to 90.
A
9
B
9.5
Practice makes perfect
We want to approximate sqrt(90) 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 90.
Number
Square of Number
8
8^2=64
9
9^2= 81
10
10^2= 100
11
11^2=121
Our table shows that 90 is between the perfect squares 81 and 100. Because 90 is closer to 81 than to 100, we can say that sqrt(90) is closer to sqrt(81) than to sqrt(100). This means that sqrt(90) is closer to 9 than to 10.
Therefore, we know that sqrt(90) is approximately 9.
Now we want to approximate sqrt(90) to the nearest tenth. We will make a table of decimal numbers between 9 and 10 whose squares are close to 90.
Number
Square of Number
9.3
9.3^2=86.49
9.4
9.4^2= 88.36
9.5
9.5^2= 90.25
9.6
9.6^2=92.16
The table shows that 90 is between 88.36 and 90.25. Because 90 is closer to 90.25 than to 88.36, we can say that sqrt(90) is closer to sqrt(90.25) than to sqrt(88.36). This means that sqrt(90) is closer to 9.5 than to 9.4.
Therefore, we know that sqrt(90) is approximately 9.5.
