Square Root of 120

The square root of a number is one of the most useful fundamental concepts in mathematics. It represents a value of a number multiplied by itself, to give the original number. In this article, we will explore the square root of 120, its properties, methods of calculation, and applications.

What is the Square Root of 120 or √𝟏𝟐𝟎 ? 

The square root of 120 is a number that equals 120, when multiplied by itself. Mathematically, it is represented as: √120 The √120 is an irrational number as it cannot be expressed in 𝑝/ 𝑞 , where 𝑝 and 𝑞 are integers and 𝑞 ≠ 0, its decimal representation is non-terminating and non-repeating. It’s approximate is: √120 = 10.9544511501 (approx.)

How to Find the Square Root of 120?  

There are several methods to calculate √120 , below, discussed some of the commonly used methods:

1. Prime Factorization Method 

Prime factorization is a method where we represent a number as a product of its prime factors. Since 120 is not a perfect square, this method will not yield an exact value but can get a simplified expression.

• Factorise 120 into its prime factors: 

120 = 2×2×2×3×5=23×3×5 

• Pairing the prime factors:

 √120 =√22×2×3×5 

• On simplifying: 

√120 =2√30 =2√30 ≈10.954 

Hence, this method is useful in showing that √120 form as 2√30 .

2. Long Division Method 

The long division method is a step-by-step approach to finding the square root of any number, especially useful in finding a square root of non-perfect squares like 120.

1. Pair the digits of 120 from right to left (120 → 1 20).
2. Find the largest number whose square is less than or equal to the first pair (1). Here, it is 1.
3. Subtract the square of this number from the first pair and bring down the next paired number (20).
4. Double the divisor and find a digit that, when added to the divisor and multiplied by the same digit, is less than or equal to the new dividend.
5. Repeat the process to get the square root and to achieve the desired level of accuracy.

3. Using a Calculator 

For quick and accurate results, a scientific calculator is the most efficient tool. Simply enter 120 and press the square root (√) button to get the approximate value: √120 =2√30 ≈10.954

Properties of Square Root of 120

1. Irrational Number: The square root of 120 is irrational because it cannot be expressed as a fraction of two integers.
2. Simplified Form: The square root of 120 can be expressed as 2√30
3. Decimal Approximation: The approximate value of √120 is 10.954.
4. Non-Perfect Square: Since 120 is not a perfect square, √120.

Applications of Square Root of 120

The square root of 120 has practical applications in various fields, including:

1. In geometry: Calculating the side lengths of squares or rectangles with an area of 120 square units.
2. In physics: Determining magnitudes in equations involving squares, such as energy or force calculations.
3. In Engineering: Solving problems related to design and measurements.
4. In finance: Used in statistical models and risk assessments.