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Last updated on May 26th, 2025

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Square Root of 601

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If a number is multiplied by itself, the result is a square. The inverse of squaring a number is taking its square root. Square roots are used in various fields such as engineering and finance. Here, we will discuss the square root of 601.

Square Root of 601 for UAE Students
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What is the Square Root of 601?

The square root is the inverse of squaring a number. 601 is not a perfect square. The square root of 601 is expressed in both radical and exponential form. In the radical form, it is expressed as √601, whereas in exponential form it is expressed as (601)^(1/2). √601 ≈ 24.5153, which is an irrational number because it cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0.

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Finding the Square Root of 601

The prime factorization method is suitable for perfect square numbers. For non-perfect square numbers like 601, the long division method and approximation method are used. Let us explore these methods:

 

  • Long division method
     
  • Approximation method
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Square Root of 601 by Long Division Method

The long division method is particularly useful for non-perfect square numbers. This method involves checking the closest perfect square number to the given number. Let us now learn how to find the square root using the long division method, step by step:

 

Step 1: Group the numbers from right to left. In the case of 601, we group it as 01 and 6.

 

Step 2: Find n whose square is less than or equal to 6. This n is 2 because 2 x 2 = 4. Subtract 4 from 6, and the remainder is 2.

 

Step 3: Bring down the next group, 01, making the new dividend 201. Double the quotient to create the new divisor: 2 x 2 = 4.

 

Step 4: Find a digit, n, such that 4n x n ≤ 201. Our choice is n = 5, as 45 x 5 = 225 is too large, but 44 x 5 = 220 is close.

 

Step 5: Subtract 220 from 201. Since there's a remainder, we continue by adding decimal places: the next dividend is 20100.

 

Step 6: Repeat the steps until the desired precision is achieved. The quotient gives us the square root: √601 ≈ 24.5153.

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Square Root of 601 by Approximation Method

The approximation method is another straightforward way to find square roots. Let us see how this applies to 601:

 

Step 1: Identify the nearest perfect squares around √601. The numbers are 576 (√576 = 24) and 625 (√625 = 25). Thus, √601 lies between 24 and 25.

 

Step 2: Apply the interpolation formula: (Value - Lower Perfect Square) / (Higher Perfect Square - Lower Perfect Square) For 601: (601 - 576) / (625 - 576) = 25/49 ≈ 0.51 Using this interpolation, we approximate √601 ≈ 24 + 0.51 = 24.51.

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Common Mistakes and How to Avoid Them in the Square Root of 601

Students often make errors while finding square roots, such as omitting the negative square root or skipping the long division steps. Let us explore common mistakes and how to avoid them.

Mistake 1

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Forgetting about the negative square root

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It is important to remember that every positive number has both a positive and negative square root. However, we generally focus on the positive square root in practical applications.

 

For example: √601 ≈ ±24.5153.

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Square Root of 601 Examples

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Max, the Girl Character from BrightChamps

Problem 1

Can you help Max find the area of a square box if its side length is given as √601?

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The area of the square is approximately 601 square units.

Explanation

The area of a square is given by side².

If the side length is √601, then the area is (√601)² = 601 square units.

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Max, the Girl Character from BrightChamps

Problem 2

A square-shaped garden has an area of 601 square feet. What is the approximate length of one side of the garden?

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Approximately 24.515 feet.

Explanation

The side length of the garden is the square root of the area. √601 ≈ 24.515 feet.

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Problem 3

Calculate √601 x 3.

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Approximately 73.5459.

Explanation

First, find √601 ≈ 24.5153, then multiply by 3: 24.5153 x 3 ≈ 73.5459.

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (600 + 1)?

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Approximately 24.5153.

Explanation

The expression simplifies to √601, which is approximately 24.5153.

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Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √601 units and the width ‘w’ is 50 units.

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Approximately 149.0306 units.

Explanation

Perimeter of a rectangle = 2 × (length + width).

Perimeter = 2 × (√601 + 50) ≈ 2 × (24.5153 + 50) ≈ 2 × 74.5153 ≈ 149.0306 units.

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FAQ on Square Root of 601

1.What is √601 in its simplest form?

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2.Mention the factors of 601.

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3.Calculate the square of 601.

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4.Is 601 a prime number?

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5.601 is divisible by?

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

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7.How can cultural or local activities in United Arab Emirates support learning Algebra topics such as Square Root of 601?

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8.How do technology and digital tools in United Arab Emirates support learning Algebra and Square Root of 601?

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

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Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 601

  • Square root: The square root of a number is a value that, when multiplied by itself, gives the original number. Example: √16 = 4.

 

  • Irrational number: An irrational number cannot be expressed as a simple fraction. It has a non-repeating, non-terminating decimal expansion.

 

  • Prime number: A number greater than 1 that is not divisible by any other numbers except 1 and itself. Example: 601.

 

  • Decimal: A number that contains a decimal point, separating the whole number from the fractional part. Example: 24.5153.

 

  • Long division method: A technique used to find the square roots of non-perfect squares. It involves dividing the number into groups and applying successive approximations.
Professor Greenline from BrightChamps

About BrightChamps in United Arab Emirates

At BrightChamps, we know algebra is more than symbols—it opens doors to endless possibilities! We’re dedicated to helping kids throughout the UAE develop crucial math skills, focusing today on the Square Root of 601 with a special focus on square roots—in an enjoyable, engaging, and easy-to-understand way. Whether your child is figuring out the speed of a roller coaster at Dubai Parks and Resorts, keeping track of local football scores, or budgeting their allowance for the latest gadgets, mastering algebra gives them confidence for everyday situations. Our interactive lessons make learning both fun and simple. Because kids in the UAE learn in varied ways, we customize our teaching to fit each child’s needs. From Dubai’s soaring skyscrapers to Abu Dhabi’s cultural heritage, BrightChamps brings math alive, making it relevant and exciting throughout the UAE. 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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