Make a table of decimal numbers whose squares are close to 105.
A
- 10
B
- 10.2
Practice makes perfect
We are asked to approximate - sqrt(105) 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 squares are close to 105.
Number
Square of Number
8
8^2=64
9
9^2=81
10
10^2= 100
11
11^2= 121
Our table shows that 105 is between the perfect squares 100 and 121. Because 105 is closer to 100 than to 121, we can say that sqrt(105) is closer to sqrt(100) than to sqrt(121). This means that sqrt(105) is closer to 10 than to 11.
We have that sqrt(105) is approximately 10. If we bring back the negative sign, we can say that - sqrt(105) is approximately - 10.
Now we want to approximate - sqrt(105) to the nearest tenth. Once again, we will ignore the negative sign for a while. We will make a table of decimal numbers between 10 and 11 whose squares are close to 105.
Number
Square of Number
10.2
10.2^2= 104.04
10.3
10.3^2= 106.09
10.4
10.4^2=108.16
10.5
10.5^2=110.25
The table shows that 105 is between 104.04 and 106.09. Because 105 is closer to 104.04 than to 106.09, we can say that sqrt(105) is closer to sqrt(104.04) than to sqrt(106.09). This means that sqrt(105) is closer to 10.2 than to 10.3.
We have that sqrt(105) is approximately 10.2. If we bring back the negative sign, we can say that - sqrt(105) is approximately - 10.2.
