Make a table of decimal numbers whose cubes are close to 310.
A
7
B
6.8
Practice makes perfect
We are asked to approximate sqrt(310) 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 cubes are close to 310.
Number
Square of Number
5
5^3=125
6
6^3= 216
7
7^3= 343
8
8^3=512
Our table shows that 310 is between the perfect cubes 216 and 343. Because 310 is closer to 343 than to 216, we can say that sqrt(310) is closer to sqrt(343) than to sqrt(216). This means that sqrt(310) is closer to 7 than to 6.
We have that sqrt(310) is approximately 7.
Now we want to approximate sqrt(310) to the nearest tenth. We will make a table of decimal numbers between 6 and 7 whose squares are close to 310.
Number
Square of Number
6.6
6.6^3=287.49
6.7
6.7^3= 300.76
6.8
6.8^3= 314.43
6.9
6.9^3=328.50
The table shows that 310 is between 300.76 and 314.43. Because 310 is closer to 314.43 than to 300.76, we can say that sqrt(310) is closer to sqrt(314.43) than to sqrt(300.76). This means that sqrt(310) is closer to 6.8 than to 6.7.
