117 LearnersLast updated on May 26th, 2025
Square Root of 719
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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 719.
What is the Square Root of 719?
The square root is the inverse of the square of the number. 719 is not a perfect square. The square root of 719 is expressed in both radical and exponential form. In the radical form, it is expressed as √719, whereas (719)^(1/2) in the exponential form. √719 ≈ 26.797, 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 719
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where long-division method and approximation method are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 719 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 719 is broken down into its prime factors.
Step 1: Finding the prime factors of 719. Since 719 is a prime number, it can only be divided by 1 and itself.
Step 2: As 719 is a prime number, it cannot be broken down further, and calculating 719 using prime factorization is not possible for finding its square root.
Square Root of 719 by Long Division Method
The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step.
Step 1: To begin with, we need to group the numbers from right to left. In the case of 719, we need to group it as 19 and 7.
Step 2: Now we need to find n whose square is ≤ 7. We can say n as ‘2’ because 2² = 4 is lesser than 7. Now the quotient is 2 after subtracting 4 from 7, the remainder is 3.
Step 3: Now let us bring down 19, making it 319 as the new dividend. Add the old divisor with the same number 2 + 2 to get 4, which will be our new divisor.
Step 4: The new divisor is 4n. We need to find the value of n.
Step 5: The next step is finding 4n × n ≤ 319. Let us consider n as 7, now 47 × 7 = 329.
Step 6: Since 329 is more than 319, consider n as 6, now 46 × 6 = 276.
Step 7: Subtract 276 from 319, the difference is 43, and the quotient is 26.
Step 8: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 4300.
Step 9: Now we need to find the new divisor that is 267 because 267 × 7 = 1869.
Step 10: Subtracting 1869 from 4300 we get the result 2431.
Step 11: Now the quotient is 26.7.
Step 12: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal values continue till the remainder is zero.
So the square root of √719 is approximately 26.79.
Square Root of 719 by Approximation Method
Approximation method is another method for finding square roots; it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 719 using the approximation method.
Step 1: Now we have to find the closest perfect square of √719. The smallest perfect square less than 719 is 676, and the largest perfect square greater than 719 is 729. √719 falls somewhere between 26 and 27.
Step 2: Now we need to apply the formula (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (719 - 676) ÷ (729 - 676) = 43/53 ≈ 0.81. Adding the value we initially got, which is 26 + 0.81 = 26.81, so the approximate square root of 719 is 26.81.
Common Mistakes and How to Avoid Them in the Square Root of 719
Students do make mistakes while finding the square root, like forgetting about the negative square root, skipping long division methods, etc. Now let us look at a few of those mistakes that students tend to make in detail.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number does have both positive and negative square roots. However, we will be taking only the positive square root, as it is the required one.
For example: √49 = 7, there is also -7 which should not be forgotten.
Mistake 2
Not adding square root symbol in proper places
Not using the square root properly is another mistake that children make. To resolve this we need to teach children that simplifying the numbers inside the square root is important and then move on to the second step.
For Example: √(9 + 16) = √9 + √16 is the wrong method of using roots.
The right way of using roots is √(9 + 16) = √25 = 5.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught to children is to simplify the numbers inside the square root. This is important so that students do not make mistakes while identifying the approximate value.
For example: √50 ≈ 7.07, not 7.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube root and square root constantly as this will help them keep away from mistakes.
For example: √64 and ∛64 are different.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps. Due to this, many students might skip a step accidentally, resulting in a wrong answer at the end of the sum. This may either happen in subtracting or elsewhere.
Square Root of 719 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √719?
The area of the square is approximately 719 square units.
Explanation
The area of the square = side².
The side length is given as √719.
Area of the square = side² = √719 × √719 = 719.
Therefore, the area of the square box is approximately 719 square units.
Problem 2
A square-shaped building measuring 719 square feet is built; if each of the sides is √719, what will be the square feet of half of the building?
359.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 719 by 2, we get 359.5.
So half of the building measures 359.5 square feet.
Problem 3
Calculate √719 × 5.
Approximately 133.985
Explanation
The first step is to find the square root of 719, which is approximately 26.797.
The second step is to multiply 26.797 by 5.
So 26.797 × 5 ≈ 133.985.
Problem 4
What will be the square root of (700 + 19)?
The square root is approximately ±26.797.
Explanation
To find the square root, we need to find the sum of (700 + 19). 700 + 19 = 719, and then √719 ≈ 26.797.
Therefore, the square root of (700 + 19) is approximately ±26.797.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √719 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 129.594 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√719 + 38) = 2 × (26.797 + 38) ≈ 2 × 64.797 ≈ 129.594 units.
FAQ on Square Root of 719
1.What is √719 in its simplest form?
2.Mention the factors of 719.
3.Calculate the square of 719.
4.Is 719 a prime number?
5.Is 719 divisible by any number other than 1 and itself?
6.How does learning Algebra help students in Saudi Arabia make better decisions in daily life?
7.How can cultural or local activities in Saudi Arabia support learning Algebra topics such as Square Root of 719?
8.How do technology and digital tools in Saudi Arabia support learning Algebra and Square Root of 719?
9.Does learning Algebra support future career opportunities for students in Saudi Arabia?
Important Glossaries for the Square Root of 719
- Square root: A square root is the inverse of a square. Example: 5² = 25, and the inverse of the square is the square root, that is √25 = 5.
- Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.
- Prime number: A prime number is a number greater than 1 with no divisors other than 1 and itself.
- Long division method: A technique used to find the square root of non-perfect squares through repeated division and subtraction.
- Approximation method: A method to find an approximate value of a square root by identifying its position between two perfect squares.
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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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