Introduction
Roots of a number are used to find the value that, when multiplied by itself a certain number of times, equals the original number. In mathematics, there are two commonly used roots: square roots and other roots. In this article, we will explore the difference between square roots and other roots and provide examples to illustrate their use.
Square Roots
A square root is a value that, when multiplied by itself, equals the original number. It is denoted using the symbol √. For instance, the number 3 is the square root of 9 because when 3 is multiplied by itself, the result is 9. The symbol for the square root of a number is √, followed by the number inside the symbol. For example, √9 = 3.
It is important to note that every positive number has two square roots: a positive and a negative square root. For instance, the two possible values for the square root of 9 are 3 and -3. The positive square root is the number that is positive and the negative square root is the number that is negative.
Check out the square root calculator
Other Roots
In addition to square roots, there are other types of roots that can be calculated, including cube roots, fourth roots, and so on. These roots are denoted using a radical symbol, with the index number indicating the type of root being taken. For example, a cube root is denoted using the symbol ∛, and a fourth root is denoted using the symbol ⁴√.
For instance, the number 3 is the cube root of 27 because when 3 is multiplied by itself three times, the result is 27. And, 2 is the fourth root of 16 because when 2 is multiplied by itself four times, the result is 16.
Finding Other Roots
To find the value of other roots, the number is divided by the root symbol. For example, to find the cube root of 27, we can write:
27^(1/3) = 3
To find the fourth root of 16, we can write:
16^(1/4) = 2
It is important to note that, like square roots, other roots can also have positive and negative values.
Find out what is the square root of 265
Applications of Roots
Roots are used in a variety of applications, including geometry, engineering, and economics. For example, in geometry, roots can be used to find the length of a side of a square or cube. In engineering, roots are used to solve problems related to energy, power, and force. In economics, roots can be used to find the square root of a number to calculate the present value of an investment.
Square Roots in Geometry
In geometry, square roots are used to find the length of a side of a square. For example, if the area of a square is 25 square units, the length of each side can be found by taking the square root of the area. The formula for the area of a square is side x side, so:
25 = side x side
By finding the square root of both sides, we obtain:
√25 = √(side x side) = side
The square root of 25 is 5, so the length of each side of the square is 5 units.
Other Roots in Geometry
The cube root of 27, which is the volume of a cube, can be used to find the length of each side of the cube. This is because the length of each side is equal to the cube root of the volume. In this case, taking the cube root of 27 gives us 3, so the length of each side of the cube is 3 units.
Similarly, fourth roots can be used in geometry to find the length of a side of a fourth power. For example, if the fourth power of a number is 16, the length of the side can be found by taking the fourth root of the number. The formula for the fourth power is side x side x side x side, so:
16 = side x side x side x side
By finding the fourth root of both sides, we get:
2 = side
Therefore, the length of the side of the fourth power is 2 units.
Read an article about Radicals and Rational Exponents
Conclusion
In conclusion, roots are an important concept in mathematics, and understanding the difference between square roots and other roots can help in solving various problems in different fields such as geometry, engineering, and economics. Square roots are used to find the value that, when multiplied by itself, equals the original number. Other roots, including cube roots and fourth roots, can also be used to find the value that, when multiplied by itself a certain number of times, equals the original number. By understanding and using roots, we can solve a wide range of problems in different areas of study.