Make a table of decimal numbers whose squares are close to 3352.
A
- 13
B
- 12.9
Practice makes perfect
We are asked to approximate - sqrt(3352) 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 write the radicand as a decimal.
335/2=167.5
We also need to ignore the negative sign for now. Let's start by making a table of numbers whose squares are close to 167.5.
Number
Square of Number
10
10^2=100
11
11^2=121
12
12^2= 144
13
13^2= 169
Our table shows that 167.5 is between the perfect squares 144 and 169. Because 167.5 is closer to 169 than to 144, we can say that sqrt(167.5) is closer to sqrt(169) than to sqrt(144). This means that sqrt(167.5) is closer to 13 than to 12.
We have that sqrt(167.5) is approximately 13. If we bring back to the fraction and the negative sign, we can say that - sqrt(3352) is approximately - 13.
Now we want to approximate - sqrt(3352) to the nearest tenth. Once again, we will rewrite the fraction as decimal and ignore the negative sign for a while. We will make a table of decimal numbers between 12 and 13 whose squares are close to 167.5.
Number
Square of Number
12.7
12.7^2=161.29
12.8
12.8^2=163.84
12.9
12.9^2= 166.41
13
13^2= 169
The table shows that 167.5 is between 166.41 and 169. Because 167.5 is closer to 166.41 than to 169, we can say that sqrt(167.5) is closer to sqrt(166.41) than to sqrt(169). This means that sqrt(167.5) is closer to 12.9 than to 13.
We have that sqrt(167.5) is approximately 12.9. If we bring back the fraction and the negative sign, we can say that - sqrt(3352) is approximately - 12.9.
