122 LearnersLast updated on May 26th, 2025
Square Root of 726
If a number is multiplied by itself, the result is a square. The inverse operation is finding the square root. The square root is used in various fields such as engineering, finance, and architecture. Here, we will discuss the square root of 726.
What is the Square Root of 726?
The square root is the inverse of squaring a number. Since 726 is not a perfect square, its square root is expressed in both radical and exponential forms. In radical form, it is expressed as √726, whereas in exponential form, it is expressed as (726)^(1/2). √726 ≈ 26.933, which is an irrational number because it cannot be expressed as a ratio of two integers.
Finding the Square Root of 726
The prime factorization method is applicable for perfect square numbers. For non-perfect squares like 726, the long division and approximation methods are often used. Let's explore these methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 726 by Prime Factorization Method
The prime factorization of a number involves expressing it as a product of prime numbers. Let's explore the prime factorization of 726.
Step 1: Finding the prime factors of 726
Breaking it down, we get 2 x 3 x 11 x 11: 2^1 x 3^1 x 11^2
Step 2: Now we have the prime factors of 726. Since 726 is not a perfect square, we cannot pair all the factors evenly. Thus, prime factorization doesn't yield an exact square root for 726.
Square Root of 726 by Long Division Method
The long division method is used for non-perfect square numbers. Here's how to find the square root of 726 using this method:
Step 1: Group the digits of 726 from right to left. We group it as 26 and 7.
Step 2: Find n whose square is closest to 7. Use n = 2 because 2 x 2 = 4, which is less than 7. The quotient is 2, and after subtracting 4 from 7, the remainder is 3.
Step 3: Bring down 26, making the new dividend 326. Double the quotient (2), giving the new divisor as 4.
Step 4: Find n such that (4n) x n ≤ 326. Let's use n = 7, giving us 47 x 7 = 329, which is too large, so let's try n = 6.
Step 5: 46 x 6 = 276. Subtract 276 from 326, leaving a remainder of 50.
Step 6: Add a decimal point and bring down two zeros, making it 5000. Use 532 x 3 = 1596, which is too large.
Step 7: Adjust n to get a closer approximation. Continuously apply these steps until you reach the desired decimal precision.
Square Root of 726 by Approximation Method
The approximation method is an easier way to estimate square roots:
Step 1: Identify the nearest perfect squares around 726. The nearest smaller perfect square is 625 (25^2), and the nearest larger is 729 (27^2). Thus, √726 is between 25 and 27.
Step 2: Use the formula for approximation: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square) Using (726 - 625) / (729 - 625) = 101 / 104 ≈ 0.971. Adding this to the base of 25: 25 + 0.971 = 25.971, so the square root of 726 is approximately 25.971.
Common Mistakes and How to Avoid Them in the Square Root of 726
Students often make mistakes when calculating square roots, such as ignoring the negative square root or skipping steps in the long division method. Let's explore some common mistakes:
Mistake 1
Forgetting about the negative square root
Students should be reminded that numbers have both positive and negative square roots. However, in most practical applications, only the positive root is used.
For example, √50 = ±7.07.
Mistake 2
Not adding the square root symbol in the correct places
Misplacing the square root symbol is a common error. It's important to simplify the expression inside the root before proceeding.
For example, √(12+24) = √36, not √12 + √24.
Mistake 3
Not finding the correct value of a non-perfect square
Start by simplifying the expression inside the square root to avoid errors in estimating non-perfect squares.
For example, the correct approximation of √50 is 7.071, not 7.
Mistake 4
Confusing the square root symbol with the cube root
It's important to distinguish between square roots and cube roots.
For example, √50 and ∛50 represent different operations.
Mistake 5
Making mistakes in long division
The long division method involves multiple steps, and students may skip a step accidentally, leading to incorrect results. Careful attention to each step is crucial.
Square Root of 726 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √726?
The area of the square is approximately 726 square units.
Explanation
The area of a square is calculated as side^2.
With a side length of √726, the area = (√726)^2 = 726 square units.
Problem 2
A square-shaped building measures 726 square feet. If each side is √726, what will be the square footage of half the building?
363 square feet
Explanation
Since the building is square-shaped, dividing the total area by 2 gives half the building's area: 726 / 2 = 363 square feet.
Problem 3
Calculate √726 x 5.
Approximately 134.665
Explanation
First, find the square root of 726, approximately 26.933, then multiply by 5: 26.933 x 5 = 134.665.
Problem 4
What will be the square root of (726 + 9)?
The square root is 27.
Explanation
Calculate the sum of (726 + 9) = 735, then find the square root: √735 ≈ 27.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √726 units and the width ‘w’ is 20 units.
The perimeter is approximately 93.866 units.
Explanation
Perimeter of a rectangle = 2 × (length + width).
Perimeter = 2 × (√726 + 20) ≈ 2 × (26.933 + 20) ≈ 2 × 46.933 = 93.866 units.
FAQ on Square Root of 726
1.What is √726 in its simplest form?
2.Mention the factors of 726.
3.Calculate the square of 726.
4.Is 726 a prime number?
5.726 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 726?
8.How do technology and digital tools in Singapore support learning Algebra and Square Root of 726?
9.Does learning Algebra support future career opportunities for students in Singapore?
Important Glossaries for the Square Root of 726
- Square root: A square root is the inverse of squaring a number. For example, 5^2 = 25, so √25 = 5.
- Irrational number: An irrational number cannot be expressed as a simple fraction. For instance, √726 is irrational.
- Perfect square: A perfect square is a number that has an integer as its square root, such as 25, whose square root is 5.
- Prime factorization: Expressing a number as a product of prime numbers, e.g., 726 = 2 x 3 x 11 x 11.
- Long division method: A step-by-step technique to find the square root of non-perfect squares.
Explore More algebra
About BrightChamps in Singapore
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
: He loves to play the quiz with kids through algebra to make kids love it.
