The square root of a number is a mathematical value that, when multiplied by itself, gives the original number. In this article, we will explore the square root of 480 and how to calculate it.
What is the Square Root of 480?
The square root of 480 is an irrational number, which means it cannot be expressed as a simple fraction. The exact value of the square root of 480 is approximately 21.9089023.
How to Calculate the Square Root of 480
There are different methods to calculate the square root of a number. One of the most common ways is to use the long division method. Here’s how to calculate the square root of 480:
- Group the digits of 480 into pairs, starting from the right: 48 and 0.
- Find the largest whole number whose square is less than or equal to 48. The largest such number is 6, since 6 x 6 = 36 and 7 x 7 = 49.
- Write 6 on top and subtract 36 from 48, which gives 12.
- Bring down the next pair of digits (0) to the right of 12 and make it 120.
- Double the number on top (6) to get 12 and put it on the left of 120 to get 12120.
- Find the largest digit that can be multiplied by 12 and added to the left of 120 to get a number less than or equal to 12120. The largest such digit is 4, since 124 x 124 = 15376.
- Write 4 on top and subtract 124 x 4 = 496 from 12120 to get 11624.
- Bring down the next pair of digits (00) to the right of 11624 and make it 116240.
- Double the number on top (64) to get 128 and put it on the left of 116240 to get 128116240.
- Find the largest digit that can be multiplied by 128 and added to the left of 116240 to get a number less than or equal to 128116240. The largest such digit is 8, since 1288 x 1288 = 1651504.
- Write 8 on top and subtract 1288 x 8 = 103040 from 128116240 to get 127113200.
- Bring down the next pair of digits (00) to the right of 127113200 and make it 12711320000.
- Double the number on top (648) to get 1296 and put it on the left of 12711320000 to get 129612711320000.
- Find the largest digit that can be multiplied by 1296 and added to the left of 12711320000 to get a number less than or equal to 129612711320000. The largest such digit is 9, since 12969 x 12969 = 167961561.
- Write 9 on top and subtract 12969 x 9 = 116721 from 129612711320000 to get 129612711203279.
Continue the process as long as necessary to get the desired level of accuracy. In practice, calculators and computers can quickly provide the square root of 480 to many decimal places.
Properties of the Square Root of 480
The square root of 480 has several interesting properties:
- The square root of 480 is an irrational number, which means it cannot be expressed as a simple fraction.
- The square root of 480 is a positive number, since 480 is a positive number.
- The square root of 480 is greater than 20 and less than 22, since 20 x 20 = 400 and 22 x 22 = 484.
- The square root of 480 can be represented as √(16 x 30), which means it is the product of the square root of 16 (which is 4) and the square root of 30.
- The square root of 480 can be approximated by the decimal 21.9089023, which is a finite decimal but not a terminating one.
- The square root of 480 corresponds to a point on the graph of the function y = √x, where x is the input (or domain) and y is the output (or range).
Applications of the Square Root of 480
The square root of 480 has various applications in real life, including:
- Engineering: The square root of 480 appears in calculations related to electrical power, such as the calculation of the root mean square (RMS) voltage or current in an AC circuit.
- Geometry: The square root of 480 appears in calculations related to the diagonal of a rectangular prism or the hypotenuse of a triangle with legs of length 16 and 30.
- Statistics: The square root of 480 appears in calculations related to the standard deviation of a data set with 480 observations.
- Finance: The square root of 480 appears in calculations related to the volatility of a financial instrument or the margin of error of a sample size of 480.
Conclusion
The square root of 480 is a mathematical value that represents the positive number that, when multiplied by itself, gives 480. It is an irrational number that can be approximated by the decimal 21.9089023. The square root of 480 has several interesting properties and applications in various fields. By understanding the concept of the square root of 480, we can deepen our understanding of mathematics and its practical uses.