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Last updated on May 26th, 2025

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Square Root of -175

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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 such as engineering and science. Here, we will discuss the square root of -175.

Square Root of -175 for Australian Students
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What is the Square Root of -175?

The square root is the inverse of the square of the number. Since -175 is a negative number, its square root is not a real number. Instead, it is expressed in terms of imaginary numbers. The square root of -175 can be expressed in radical form as √(-175) or as 5i√7, where i is the imaginary unit.

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Understanding the Square Root of -175

For negative numbers, the square root involves the imaginary unit "i," which is defined as √(-1). The square root of -175 can be found by factoring -175 into -1 and 175. We express this as √(-175) = √(-1×175) = √(-1)×√(175) = i√175. Since 175 = 5×5×7, we can further simplify this to 5i√7.

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Square Root of -175 by Prime Factorization Method

The prime factorization of 175 is 5×5×7. To express the square root of -175 using prime factorization:

 

Step 1: Factor 175 into prime factors: 5×5×7.

 

Step 2: To find the square root of -175, express it as √(-1×5×5×7).

 

Step 3: Simplify the square root of the positive part: √(5×5×7) = 5√7.

 

Step 4: Combine with the imaginary unit: √(-175) = i×5√7 = 5i√7.

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Square Root of -175 by Approximation Method

Approximation for imaginary numbers involves estimating the absolute value and then multiplying by i:

 

Step 1: First, approximate the square root of the absolute value, 175.

 

Step 2: Since 175 is between 144 (12^2) and 196 (14^2), we approximate √175 ≈ 13.2.

 

Step 3: Combine with the imaginary unit: The approximate value of √(-175) is 13.2i.

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Common Mistakes and How to Avoid Them in the Square Root of -175

Students often make errors when working with the square root of negative numbers, such as ignoring the imaginary unit or incorrectly simplifying expressions. Let’s look at some common mistakes and how to avoid them.

Mistake 1

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Ignoring the Imaginary Unit

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When dealing with negative numbers under a square root, students often forget to include the imaginary unit, i. Remember, √(-1) = i.

For example, √(-9) should be written as 3i, not just 3.

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Square Root of -175 Examples

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Max, the Girl Character from BrightChamps

Problem 1

Can you help Max find the magnitude of a vector if its component along one axis is √(-175)?

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The magnitude is 5√7.

Explanation

The magnitude of a vector with an imaginary component is the absolute value. If the component is √(-175), the magnitude is |5i√7| = 5√7.

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Problem 2

Calculate √(-175) × 2.

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The result is 10i√7.

Explanation

First, find the square root of -175, which is 5i√7.

Then multiply by 2: 5i√7 × 2 = 10i√7.

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Max, the Girl Character from BrightChamps

Problem 3

What is the square of √(-175)?

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The square is -175.

Explanation

Squaring the square root returns the original number: (√(-175))^2 = -175.

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FAQ on Square Root of -175

1.What is √(-175) in terms of i?

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2.What are the prime factors of 175?

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3.Is the square root of -175 a real number?

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4.What is the absolute value of √(-175)?

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5.How do you express √(-175) using imaginary numbers?

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

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7.How can cultural or local activities in Australia support learning Algebra topics such as Square Root of -175?

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8.How do technology and digital tools in Australia support learning Algebra and Square Root of -175?

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

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Important Glossaries for the Square Root of -175

  • Square root: The inverse operation of squaring a number. For negative numbers, involves imaginary numbers.

 

  • Imaginary unit (i): The unit used to express the square root of negative numbers, defined as √(-1).

 

  • Complex number: A number comprising a real part and an imaginary part, such as a + bi.

 

  • Prime factorization: Breaking down a number into its prime factors, useful for simplifying square roots.

 

  • Absolute value: The non-negative value of a number without regard to its sign, used to express magnitudes.
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About BrightChamps in Australia

At BrightChamps, we believe algebra is more than symbols—it opens doors to endless opportunities! Our mission is to help children all over Australia gain important math skills, focusing today on the Square Root of -175 with a special emphasis on understanding square roots—in a lively, fun, and easy-to-grasp way. Whether your child is calculating the speed of a roller coaster at Luna Park Sydney, tracking cricket match scores, or managing their allowance for the newest gadgets, mastering algebra gives them the confidence to tackle everyday problems. Our interactive lessons make learning both simple and enjoyable. Since children in Australia learn in various ways, we adapt our approach to fit each learner’s style. From Sydney’s vibrant streets to the stunning Gold Coast beaches, BrightChamps brings math to life, making it relevant and exciting throughout Australia. Let’s make square roots a joyful part of 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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Max, the Girl Character from BrightChamps

Fun Fact

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

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