122 LearnersLast updated on May 26th, 2025
Square Root of 694
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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 694.
What is the Square Root of 694?
The square root is the inverse of the square of the number. 694 is not a perfect square. The square root of 694 is expressed in both radical and exponential form. In the radical form, it is expressed as √694, whereas 694^(1/2) in the exponential form. √694 ≈ 26.342, 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 694
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers, where the 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 694 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 694 is broken down into its prime factors.
Step 1: Finding the prime factors of 694
Breaking it down, we get 2 x 347. 694 = 2^1 x 347^1
Step 2: Now we found out the prime factors of 694. The second step is to make pairs of those prime factors. Since 694 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating 694 using prime factorization is not feasible for finding its square root.
Square Root of 694 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 694, we write it as 6 and 94.
Step 2: Now, find n whose square is less than or equal to 6. We take n as ‘2’ because 2 x 2 = 4, which is less than 6. The quotient is 2, and after subtracting 4 from 6, the remainder is 2.
Step 3: Bring down 94, making the new dividend 294. Add the old divisor with the same number, 2 + 2, to get 4, which will be our new divisor.
Step 4: The new divisor will be the sum of the previous quotient and double it. We have 4n as the new divisor; we need to find n such that 4n x n ≤ 294.
Step 5: Let n be 6, so 46 x 6 = 276, which is less than 294.
Step 6: Subtract 276 from 294; the difference is 18, and the quotient becomes 26.
Step 7: 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 1800.
Step 8: Now find the new divisor, which is 526. When 526 is multiplied by 3, we get 1578.
Step 9: Subtracting 1578 from 1800 gives us 222.
Step 10: The quotient so far is 26.3.
Step 11: Continue these steps until we get two decimal places or until the remainder is zero.
So the square root of √694 is approximately 26.34.
Square Root of 694 by Approximation Method
The 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 694 using the approximation method.
Step 1: Find the closest perfect squares around √694. The smallest perfect square less than 694 is 676, and the largest perfect square greater than 694 is 729. √694 falls somewhere between 26 and 27.
Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) (694 - 676) / (729 - 676) = 18 / 53 ≈ 0.34 Using the formula, we identified the decimal point of our square root. Adding this to the whole number gives us 26 + 0.34 = 26.34, so the square root of 694 is approximately 26.34.
Common Mistakes and How to Avoid Them in the Square Root of 694
Students do make mistakes while finding the square root, such as forgetting about the negative square root and skipping long division methods. 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: √50 ≈ 7.07, there is also -7.07 which should not be forgotten.
Mistake 2
Not adding the 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 before moving on to the second step.
For example: √(12+24) = √12 + √24 is the wrong method.
The right way is √(12+24) = √36.
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 is wrong; the correct answer is √50 ≈ 7.071.
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 avoid mistakes.
For example: √50 and ∛50 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. This may either happen while subtracting or elsewhere.
Square Root of 694 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √694?
The area of the square is approximately 694 square units.
Explanation
The area of the square = side^2. The side length is given as √694.
Area of the square = side^2 = √694 x √694 = 694.
Therefore, the area of the square box is approximately 694 square units.
Problem 2
A square-shaped building measuring 694 square feet is built; if each of the sides is √694, what will be the square feet of half of the building?
347 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 694 by 2, we get 347.
So half of the building measures 347 square feet.
Problem 3
Calculate √694 x 5.
131.71
Explanation
The first step is to find the square root of 694, which is approximately 26.34.
The second step is to multiply 26.34 by 5.
So 26.34 x 5 = 131.71.
Problem 4
What will be the square root of (694 + 6)?
The square root is approximately 26.
Explanation
To find the square root, we need to find the sum of (694 + 6). 694 + 6 = 700, and then √700 ≈ 26.46.
Therefore, the square root of (694 + 6) is approximately ±26.46.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √694 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 128.68 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√694 + 38) = 2 × (26.34 + 38) = 2 × 64.34 = 128.68 units.
FAQ on Square Root of 694
1.What is √694 in its simplest form?
2.Mention the factors of 694.
3.Calculate the square of 694.
4.Is 694 a prime number?
5.694 is divisible by?
6.How does learning Algebra help students in Qatar make better decisions in daily life?
7.How can cultural or local activities in Qatar support learning Algebra topics such as Square Root of 694?
8.How do technology and digital tools in Qatar support learning Algebra and Square Root of 694?
9.Does learning Algebra support future career opportunities for students in Qatar?
Important Glossaries for the Square Root of 694
- Square root: A square root is the inverse of a square. Example: 4^2 = 16, and the inverse of the square is the square root, that is √16 = 4.
- 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.
- Principal square root: A number has both positive and negative square roots; however, it is always the positive square root that is more commonly used in practical applications. This is known as the principal square root.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 12 is 2^2 x 3.
- Long division method: A technique used to divide numbers to find the square root of non-perfect squares involving repeated division steps.
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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
: He loves to play the quiz with kids through algebra to make kids love it.
