How Square Roots can be Applied in Real Life Situations

A square root is a number that is the inverse value of a squaring number. The square of any number can be defined as the number that is obtained by multiplying a number with itself. The representation of a square is – consider c as the square root of d. For this statement, c x c = d. All square roots have two values – a positive and a negative value. Hence, c and -c are the square roots of d. In mathematical terms, a square root is described as a factor of a number that is multiplied by itself to give the initial value of the number. Square roots are regarded as special exponents. A square root is symbolised by . The symbol of square () is known by a unique term called radical, while the number present under the square root is called the radicand. Square roots are only used in mathematics, but are also applied in real-life situations. The sections below will highlight the question – what is a square root used for.

Square root properties 

This segment will elucidate the properties of a square root: 

• A perfect square root persists only for a perfect square number
• For an even perfect square, an even square root will be procured. Similarly, when there is an odd perfect square, an odd square root will be procured
• For negative numbers, square roots are undefined
• For a number containing an odd number of zeroes, the square root is not possible
• Square root can only be found only if there are an even number of zeroes
• It is possible to multiply two square root numbers. Example – 7 2 = 14

Examples of square roots

A few examples of square roots have been elucidated below:

In mathematics, x = y2 is the representation for y being a square root of number x .

Example 1: Find the square roots of 49 .

For 49, both 7 and -7 are the square roots.

Because 7 x 7 = -7 x -7 = 49 

Here, 49 is called the radicand, and the square root is known as radical. 

A square root has an exponential power of ½. 

Example 2: Find the square root of 144. 

For 144, 12 and -12 are the square roots .

As 12 x 12 and -12 x 12 both give 144 .

Here, 144 is called the radicand .

Methods to find the square root 

To find square roots for every number other than perfect squares is not that easy. Perfect squares are positive integers that are obtained by multiplying the integer by itself. The perfect squares have an exponential power of 2. The four major methods that are implemented to obtain a square root of any number are: 

• Repeated subtraction method 
• Prime Factorization 
• Estimation method 
• Long division method of finding square roots 

What is a square root used for?

This segment of this article will focus on the uses of square roots. Square roots are applied in my disciplines such as engineering, finance, probability, architecture, and physics. 

• In the field of finance

The rate of return on an asset in a period of 2 units ( 2 years, 2 months, etc.) is found by using square roots. 

The formula used in this situation is 

R = V2V0 – 1

Here, R denotes the return rate annually 

V0 denotes the initial value 

V2 denoted the money value after 2 years.

• Square roots are applied in normal distributions 

Square roots are observed in the probability density function. The formula used in this situation is 

 12e–12( x – )2

In this formula, denotes the mean

  denotes the standard deviation and 2 denotes the variance. 

• The connection between square roots & the Pythagorean theorem

The Pythagoras theorem is applied in 

1. Engineering 
2. Architecture 
3.  Carpentry 
4. Construction
5. Graphics 

The Pythagorean theorem is applied only to right-angled triangles. 

The formula used in this case is 

A 2 + B2 = C2 

Here, A and B denote the two shorter sides of the triangle and C denoted the hypotenuse 

If the value for any two sides of a right-angled triangle is known but the third side is unknown, it can be found by using this formula. 

• Square roots are applied to find the distance between 2 distinct points in 2-D or 3-D systems 

The formula that is implemented in 2-D to analyse the distance from ( x1y1) to (x2y2) is 

D = ((x2– x1)2 + (y2– y1)2)

The formula implemented for 3-D to analyse the distance from ( x1y1z1) to (x2y2z2) is 

D = (( x2–x1)2+ (y2– y1)2 +( z2_– z1)2)

• The quadratic formula uses square roots 

To solve any quadratic equation, we have to apply the quadratic formula. 

A quadratic formula is always of the form ax2 + bx + c = 0

Here, a and b cannot be zero .

The formula to solve this equation is 

x = -b b2– 4ac2a

The rules for this are

1. If b2– 4ac > 0 there are two real and distinct solutions are present for the equation.
2. If b2– 4ac < 0 two complex conjugate answers are present for the equation. 
3. If b2– 4ac = 0 means the presence of one real but a repeated solution for the equation.

Conclusion 

A square root is described as a special exponent that is multiplied by itself to give back the original value. It is represented with the symbol . The terminologies used in the square root are – radical and radicand. The symbol of square () is known by a unique term called radical, while the number that is present under the square root is called the radicand. A few properties of square roots are – only when an even number of zeroes are present in a number the square root can be found, negative numbers cannot have square roots, and multiplication between two square roots is possible. A few methods that are used to find square roots are – the repeated subtraction method, the prime factorization, the estimation method, and the long division method of finding square roots. This article has answered the question – what is a square root used for.