Last Updated : 16 May, 2024

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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.

A square root is an important tool that is used in different domains like designing structures, calculating areas, solving complex calculations, and many more. In this article, we will study some real-life applications of square roots.

## What is Square Root ?

Square root is like asking the question: "What number multiplied by itself gives me the original number?"

Square root of a number is a number which when multiplied by itself gives the original number. ** For example, square root of 9 = √9 = 3**. General representation of square root is square root of

**n = √n**## Applications of Square Root

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

Field of engineering widely uses the concept of 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 (x_{1}, y_{1}, z_{1}) and (x_{2}, y_{2}, z_{2}) = √(x_{1 }- x_{2})^{2 }+ (y_{1 }- y_{2})^{2 }+ (z_{1 }- z_{2})^{2}

### In Mathematical Concepts

Since, 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 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 ax^{2 }+ bx + c = 0

Roots are calculated using x_{1} = (-b+ √(b^{2}-4ac))/2a

x_{2}= (-b - √(b^{2}-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.∑ (R_{i}-R')^{2})

Where,

- N is the number of observations
- R
_{i}is the return for the i^{th}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

## Use of Square Root

The square root finds application in various real-world scenarios:

- Mathematics: In arithmetic and algebra, square roots are used to solve equations, calculate areas and volumes, and find unknown values. For example, in geometry, the square root is used to determine the side length of a square given its area.

- Engineering: Engineers use square roots in calculations involving measurements, dimensions, and forces. For instance, in structural engineering, the square root is used to calculate the magnitude of forces or stresses acting on materials like steel or concrete.

- Finance: Square roots are utilized in financial analysis, particularly in risk assessment and portfolio management. They are used to calculate standard deviation, a measure of investment risk, and to model financial data distributions.

- Physics: In physics, square roots are employed to analyze phenomena such as motion, energy, and waves. For example, in mechanics, square roots are used to calculate velocities or accelerations in kinematic equations.

- Computer Science: Square roots are used in algorithms and computer programming for tasks like numerical analysis, cryptography, and signal processing. They are essential in algorithms for calculations involving distance, optimization, and error correction.

## Applications of square root - FAQs

### What is the representation of the square root of a number?

Square root is represented by the square root symbol √ . We can also use the half-power representation as n

^{1/2}

**What is the significance of square roots in real life?**

**What is the significance of square roots in real life?**

Square roots help us solve problems involving areas, such as figuring out the side length of a square or the length of a diagonal in a rectangle.

### How is the square root used in mathematical concepts?

Square root is widely used in mathematical concepts for calculation of complex results like square root of a number, distance between two or more points and for using Pythagoras rule in triangles.

**Can square roots be useful in finance?**

**Can square roots be useful in finance?**

Yes, square roots are used in finance for risk assessment and volatility calculations, helping investors understand the uncertainty associated with their investments.

**How do square roots apply in physics?**

**How do square roots apply in physics?**

Square roots are used in physics to calculate magnitudes of vectors, such as determining the velocity of an object or the intensity of a force.

### What is the use of square root in distribution curves?

Distribution curves are used in probability to interpret the probability of occurrence of events for a continuous function. These curves like normal distribution curves use square roots in their representation.

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