Make a table of decimal numbers whose squares are close to 46.
A
7
B
6.8
Practice makes perfect
We are asked to approximate sqrt(46) 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 squares are close to 46.
Number
Square of Number
4
4^2=16
5
5^2=25
6
6^2= 36
7
7^2= 49
Our table shows that 46 is between the perfect squares 36 and 49. Because 46 is closer to 49 than to 36, we can say that sqrt(46) is closer to sqrt(49) than to sqrt(36). This means that sqrt(46) is closer to 7 than to 6.
We have that sqrt(46) is approximately 7.
Now we want to approximate sqrt(46) to the nearest tenth. We will make a table of decimal numbers between 6 and 7 whose squares are close to 46.
Number
Square of Number
6.6
6.6^2=43.56
6.7
6.7^2= 44.89
6.8
6.8^2= 46.24
6.9
6.9^2=47.61
The table shows that 46 is between 44.89 and 46.24. Because 46 is closer to 46.24 than to 44.89, we can say that sqrt(46) is closer to sqrt(46.24) than to sqrt(44.89). This means that sqrt(46) is closer to 6.8 than to 6.7.
