Make a table of decimal numbers whose cubes are close to 25.
A
3
B
2.9
Practice makes perfect
We are asked to approximate sqrt(25) 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. Let's start by making a table of numbers whose cubes are close to 25.
Number
Cube of Number
1
1^3=1
2
2^3= 8
3
3^3= 27
4
4^3=64
Our table shows that 25 is between the perfect cubes 8 and 27. Because 25 is closer to 27 than to 8, we can say that sqrt(25) is closer to sqrt(27) than to sqrt(8). This means that sqrt(25) is closer to 3 than to 2.
Therefore, we have that sqrt(25) is approximately 3.
Now, we want to approximate sqrt(25) to the nearest tenth.
We will make a table of decimal numbers between 2 and 3 whose cubes are close to 25.
Number
Square of Number
2.7
2.7^3=19.68
2.8
2.8^3=21.95
2.9
2.9^3= 24.40
3
3^3= 27
The table shows that 25 is between 24.40 and 27. Because 25 is closer to 24.40 than to 27, we can say that sqrt(25) is closer to sqrt(24.40) than to sqrt(27). This means that sqrt(25) is closer to 2.9 than to 3.
Therefore, we have that sqrt(25) is approximately 2.9.
