Make a table of decimal numbers whose squares are close to 274.
A
3
B
2.6
Practice makes perfect
We are asked to approximate sqrt(274) 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.
27/4=6.75
Let's start by making a table of numbers whose squares are close to 6.75.
Number
Square of Number
1
1^2=1
2
2^2= 4
3
3^2= 9
4
4^2=16
Our table shows that 6.75 is between the perfect squares 4 and 9. Because 6.75 is closer to 9 than to 4, we can say that sqrt(6.75) is closer to sqrt(9) than to sqrt(4). This means that sqrt(6.75) is closer to 3 than to 2.
Therefore, we have that sqrt(6.75) is approximately 3. If we bring back to the fraction, we can say that sqrt(274) is approximately 3.
Now we want to approximate sqrt(274) to the nearest tenth. Once again, we will rewrite the fraction as decimal for a while. We will make a table of decimal numbers between 2 and 3 whose squares are close to 274.
Number
Square of Number
2.3
2.3^2=5.29
2.4
2.4^2=5.76
2.5
2.5^2= 6.25
2.6
2.6^2= 6.76
The table shows that 6.75 is between 6.25 and 6.76. Because 6.75 is closer to 6.76 than to 6.25, we can say that sqrt(6.75) is closer to sqrt(6.76) than to sqrt(6.25). This means that sqrt(6.75) is closer to 2.6 than to 2.5.
Therefore, we have that sqrt(6.75) is approximately 2.6. If we bring back the fraction, we can say that sqrt(274) is approximately 2.6.
