126 LearnersLast updated on May 26th, 2025
Square Root of 601
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.
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.
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
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.
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.
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
Forgetting about the negative square root
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.
Mistake 2
Not adding the square root symbol in proper places
A common mistake is incorrect placement of the square root symbol. Always simplify expressions within the square root before proceeding.
For example: √(25 + 36) ≠ √25 + √36. The correct expression is √(25 + 36) = √61.
Mistake 3
Not finding the correct value of a non-perfect square
Students should first simplify the numbers under the square root to avoid mistakes.
For example: √601 ≈ 24.5153, not simply 24 or 25.
Mistake 4
Confusing the square root symbol with the cube root
Always differentiate between square roots and cube roots.
For example: √601 and ∛601 are not the same.
Mistake 5
Making mistakes in long division
The long division method involves multiple steps where students can easily make errors, such as incorrect subtraction or misplacing decimals. Careful tracking of each step is crucial.
Square Root of 601 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √601?
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.
Problem 2
A square-shaped garden has an area of 601 square feet. What is the approximate length of one side of the garden?
Approximately 24.515 feet.
Explanation
The side length of the garden is the square root of the area. √601 ≈ 24.515 feet.
Problem 3
Calculate √601 x 3.
Approximately 73.5459.
Explanation
First, find √601 ≈ 24.5153, then multiply by 3: 24.5153 x 3 ≈ 73.5459.
Problem 4
What will be the square root of (600 + 1)?
Approximately 24.5153.
Explanation
The expression simplifies to √601, which is approximately 24.5153.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √601 units and the width ‘w’ is 50 units.
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.
FAQ on Square Root of 601
1.What is √601 in its simplest form?
2.Mention the factors of 601.
3.Calculate the square of 601.
4.Is 601 a prime number?
5.601 is divisible by?
6.How does learning Algebra help students in Singapore make better decisions in daily life?
7.How can cultural or local activities in Singapore support learning Algebra topics such as Square Root of 601?
8.How do technology and digital tools in Singapore support learning Algebra and Square Root of 601?
9.Does learning Algebra support future career opportunities for students in Singapore?
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.
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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.
Fun Fact
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