Make a table of decimal numbers whose squares are close to 175.
A
13
B
13.2
Practice makes perfect
We want to approximate sqrt(175) 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 175.
Number
Square of Number
12
12^2=144
13
13^2= 169
14
14^2= 196
15
15^2=225
Our table shows that 175 is between the perfect squares 169 and 196. Because 175 is closer to 169 than to 196, we can say that sqrt(175) is closer to sqrt(169) than to sqrt(196). This means that sqrt(175) is closer to 13 than to 14.
Therefore, we know that sqrt(175) is approximately 13.
Now we want to approximate sqrt(175) to the nearest tenth. We will make a table of decimal numbers between 13 and 14 whose squares are close to 175.
Number
Square of Number
13.1
13.1^2=171.61
13.2
13.2^2= 174.24
13.3
13.3^2= 176.89
13.4
13.4^2=179.56
The table shows that 175 is between 174.24 and 176.89. Because 175 is closer to 174.24 than to 176.89, we can say that sqrt(175) is closer to sqrt(174.24) than to sqrt(176.89). This means that sqrt(175) is closer to 13.2 than to 13.3.
Therefore, we know that sqrt(175) is approximately 13.2.
