Question

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1. What is square root and cube root function?

2. Who discovered square root and cube root function?

3. Where is square root and cube root function used in real life?

Answer 1

Step-by-step explanation:

1.The square root function is a mathematical function that returns the positive number that, when multiplied by itself, gives the original number. It can be represented using the symbol √ or using the exponent 1/2. The cube root function is a mathematical function that returns the number that, when multiplied by itself three times, gives the original number. It can be represented using the symbol ∛ or using the exponent 1/3.

2.The ancient civilizations of Babylonia, Greece, and India all independently discovered the square root function. The concept of cube root was first mentioned in the ancient Indian text "Sulbasutras" around 800 BCE. The Greek mathematician Euclid also described the cube root function in his work "Elements" around 300 BCE.

3.The square root function is used in many areas of mathematics and science, including geometry, trigonometry, and physics. In real life, square root functions are used in many areas such as engineering, architecture, and finance. For example, in engineering, square root functions are used to calculate the stress and strain on materials. In architecture, square root functions are used to calculate the area of a building or room. In finance, square root functions are used to calculate the volatility of an asset. Similarly, cube root function is used in mathematics, physics, engineering, economics, and other fields. It is used to find the cube root of a number, to find the volume of a cube, to solve equations, and to calculate the cube root of a complex number.

Answer 2

Square root and cube root functions respectively find a number that, when multiplied by itself two or three times, yields the original number. They have been used since ancient times by civilizations like the Babylonians and Greeks for problem-solving. Today, they are crucial in architecture, engineering, and physics, particularly in solving equilibrium problems.

Step-by-step explanation:

Understanding Square Root and Cube Root Functions

The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3, because 3 times 3 equals 9. The symbol for square root is √. The cube root function is similar but involves three multiples instead of two. The cube root of 27 is 3 because 3 times 3 times 3 equals 27, and the symbol for cube root is ∛.

Historical Context of Square and Cube Roots

The discovery of square roots and cube roots can be traced back to ancient civilizations like the Babylonians, Greeks, and Indians, who developed methods for estimating and calculating these roots for practical and geometric problem-solving. No single person is credited with their discovery.

Real-World Applications

In real life, square and cube roots are used in various fields, including architecture, engineering, and physics. For example, architects use square roots when calculating the dimensions for squares and rectangles in design. In physics, equilibrium problems may require finding square or cube roots when analyzing forces and moments to determine system balances. It is important to know how to perform such calculations manually or with a calculator.