The square root of a number is like the "opposite" of squaring that number. It's the value you multiply by itself to get the original number back. For example, the square root of 25 is 5 because 5 times 5 equals 25. It's represented using a radical symbol (√) followed by the number.
The square root is commonly used in calculating complex determinants or designing vehicles and infrastructures such that they can work optimally under extreme circumstances. It is necessary to understand how the concept of square root is used in real life; therefore, let us study some of its real-life applications one by one.
In Designing Things
The field of engineering widely uses the concept of the square root to design efficient engineering structures. Fields like Engineering, Architecture, Carpentry, and Construction use the square root for various purposes.
For example,
Distance Approximation: While designing real-life structures the distance between poles, tiles, and corners is very necessary. The square root is the tool which is used for calculating the distance between points in 3D structures. This is done using the formula
Distance between (x1, y1, z1) and (x2, y2, z2) = √(x1 - x2)2 + (y1 - y2)2 + (z1 - z2)2
In Mathematical Concepts
Since the square root is one of the basic concepts taught in mathematics, it forms the base of mathematical concepts and is used in various other mathematical formulas. If you carefully study the concepts like roots of an equation, the distance between 2-D objects, and the calculation of the area of mathematical figures, then you will realize that all these concepts use square roots for solving purposes.
For example, Let us see how the square root is used in the calculation of roots.
For an equation ax2 + bx + c = 0
Roots are calculated using x1 = (-b+ √(b2-4ac))/2a
x2 = (-b - √(b2-4ac))/2a
In Finance
Field of finance involves calculating some important figures like interest rate, compound interest, and total amount to assess the profits and loss within a certain duration. These calculations require the use of square root since many formulas are dependent on the square root.
For example,
Standard Deviation: Standard deviation is an important quantity used in finance to study the risk associated with a certain payment. The standard deviation for a single observation is calculated using,
Standard Deviation(σ) = √(1/N.∑ (Ri -R')2)
Where,
- N is the number of observations
- Ri is the return for the ith observation
- R' is the mean return
In Probability and Statistics
Calculation of probability and statistics involves the calculation of various distribution curves for any given function. The most common distribution curve used in probability is normal distribution which uses square root.
For example, the formula used for calculating the normal distribution.
Normal distribution of a given function is f(x) = 1/(σ√2π). e−1/2((x-μ)/σ)2
Where,
- μ is mean
- σ is standard deviation
- e is a constant
In Study of Motion
Different objects experience different types of motions which are studied in physics, one such motion is Simple Harmonic Motion. Objects like spring and pendulum depict this motion and the concept is studied with the help of square root. The oscillatory motion results in quantities like frequency and time period which are calculated using square root.
For example, An object pursuing SHM, the angular frequency and time period can be given by:
Angular frequency(ω)= √k/m
Time Period(T)= 2?√m/k