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Last updated on April 9th, 2025

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Square Root of -120

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If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in various fields, including vehicle design and finance. Here, we will discuss the square root of -120.

Square Root of -120 for UK Students
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What is the Square Root of -120?

The square root is the inverse of the square of the number. Since -120 is negative, it does not have a real square root. The square root of a negative number is an imaginary number. In the complex number system, the square root of -120 can be expressed as √(-120) = √(120) × i, where i is the imaginary unit, equal to the square root of -1. Therefore, the square root of -120 is an imaginary number.square root of minus 120

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Finding the Square Root of -120

To find the square root of a negative number like -120, we must use the concept of imaginary numbers. The square root of -120 can be represented in terms of √120 and i. Let's explore the methods used for finding the square root of the positive part:

 

  • Approximation method
  • Prime factorization method
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Square Root of -120 by Approximation Method

The approximation method is useful for finding square roots of non-perfect squares. Here, we will approximate the square root of 120 and then include the imaginary unit.

 

Step 1: Identify the closest perfect squares to 120. The perfect squares nearest to 120 are 100 and 121. Thus, √120 is between 10 and 11.

 

Step 2: Estimate the decimal value using the formula: (Given number - smaller perfect square) ÷ (larger perfect square - smaller perfect square) (120 - 100) ÷ (121 - 100) = 20 ÷ 21 ≈ 0.95

 

Step 3: Add this decimal to the smaller integer root: 10 + 0.95 = 10.95

Therefore, the square root of 120 is approximately 10.95, and the square root of -120 is approximately 10.95i.

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Square Root of -120 by Prime Factorization Method

Prime factorization is another method for finding square roots, mainly for perfect squares. Though 120 is not a perfect square, we can factor it for better understanding.

 

Step 1: Factor 120 into prime factors: 120 = 2 × 2 × 2 × 3 × 5 = 2^3 × 3 × 5

 

Step 2: Pair the factors: Since 120 is not a perfect square, it cannot be paired completely, but we can find the square root of 120 as: √120 = √(2^2 × 3 × 5 × 2) = 2√(30)

Thus, the square root of -120 is expressed in terms of i: √(-120) = 2√(30) × i

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Imaginary Numbers in Square Roots

Imaginary numbers play a crucial role in square roots of negative numbers. The imaginary unit i is defined as √(-1). Therefore, any square root of a negative number can be expressed using i.

 

For example, √(-120) = 2√(30) i.

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Common Mistakes and How to Avoid Them in the Square Root of -120

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Square Root of -120 Examples

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Problem 1

What is the square root of -120 in terms of i?

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Explanation

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Problem 2

If a square has an area of -120 square units, what is the side length?

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Explanation

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Problem 3

Calculate 5 times the square root of -120.

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Explanation

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Problem 4

What is the result of adding √(-120) and √120?

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Explanation

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Problem 5

Find the perimeter of a rectangle if its length is √(-120) units and width is 38 units.

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Explanation

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FAQ on Square Root of -120

1.What is √(-120) in its simplest form?

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2.Does -120 have a real square root?

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3.What is an imaginary unit?

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4.Can √(-120) be a real number?

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5.Why is √(-120) expressed with i?

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6.How does learning Algebra help students in United Kingdom make better decisions in daily life?

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7.How can cultural or local activities in United Kingdom support learning Algebra topics such as Square Root of -120?

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8.How do technology and digital tools in United Kingdom support learning Algebra and Square Root of -120?

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9.Does learning Algebra support future career opportunities for students in United Kingdom?

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Important Glossaries for the Square Root of -120

  • Imaginary Number: A number that can be written as a real number multiplied by the imaginary unit i, where i is the square root of -1.
     
  • Complex Number: A number composed of a real part and an imaginary part, expressed as a + bi.
     
  • Square Root: The value that, when multiplied by itself, gives the original number. For negative numbers, it involves the imaginary unit.
     
  • Prime Factorization: The process of breaking down a number into its smallest prime factors.
     
  • Approximation Method: A method to estimate the square root of non-perfect squares by identifying the closest perfect squares and using a formula to find a decimal approximation.
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About BrightChamps in United Kingdom

At BrightChamps, we believe algebra goes beyond symbols—it unlocks countless opportunities! Our mission is to help children throughout the United Kingdom develop essential math skills, focusing today on the Square Root of -120 with an emphasis on understanding square roots—in a lively, enjoyable, and straightforward way. Whether your child is figuring out the speed of a roller coaster at Alton Towers, tallying scores at a local football match, or managing their pocket money for the newest gadgets, mastering algebra gives them the confidence for everyday challenges. Our interactive lessons keep learning simple and enjoyable. Because children in the UK learn differently, we adapt our approach to fit each child’s unique needs. From the bustling streets of London to the scenic Cornish coasts, BrightChamps makes math relatable and exciting throughout the UK. Let’s bring square roots into every child’s math journey!
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Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

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Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.

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