125 LearnersLast updated on May 26th, 2025
Square Root of 676
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 676.
What is the Square Root of 676?
The square root is the inverse of the square of the number. 676 is a perfect square. The square root of 676 is expressed in both radical and exponential form. In the radical form, it is expressed as √676, whereas (676)^(1/2) in the exponential form. √676 = 26, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 676
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, 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 676 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 676 is broken down into its prime factors.
Step 1: Finding the prime factors of 676 Breaking it down, we get 2 x 2 x 13 x 13: 2^2 x 13^2
Step 2: Now we found out the prime factors of 676. The second step is to make pairs of those prime factors. Since 676 is a perfect square, the digits of the number can be grouped in pairs.
Therefore, calculating √676 using prime factorization gives us 26.
Square Root of 676 by Long Division Method
The long division method is particularly used for non-perfect square numbers, but it can also verify perfect squares. 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 676, we need to group it as 76 and 6.
Step 2: Now we need to find n whose square is 6. We can say n as ‘2’ because 2 x 2 = 4 is lesser than 6. Now the quotient is 2, after subtracting 6 - 4, the remainder is 2.
Step 3: Now let us bring down 76, which is the new dividend. Add the old divisor with the same number 2 + 2, we get 4, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 4n as the new divisor, we need to find the value of n.
Step 5: The next step is finding 4n × n ≤ 276. Let us consider n as 6, now 4 x 6 x 6 = 276.
Step 6: Subtract 276 from 276, the difference is 0, and the quotient is 26.
So the square root of √676 is 26.
Square Root of 676 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 676 using the approximation method.
Step 1: Now we have to find the closest perfect square of √676. Since 676 is a perfect square, it falls directly at 26.
Step 2: No further steps are needed as 676 is a perfect square, and its square root is already an integer.
Common Mistakes and How to Avoid Them in the Square Root of 676
Students do make mistakes while finding the square root, such as forgetting about the negative square root or 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: √676 = 26, there is also -26, 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: √(16 + 9) ≠ √16 + √9. The right way of using roots is √(16 + 9) = √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 ≈ 7.071, 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 avoid mistakes.
For Example: √64 ≠ ∛64.
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, which results in a wrong answer at the end of the sum. This may either happen in subtracting or elsewhere.
Square root of 676 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √576?
The area of the square is 576 square units.
Explanation
The area of the square = side².
The side length is given as √576.
Area of the square = side² = √576 x √576 = 24 x 24 = 576.
Therefore, the area of the square box is 576 square units.
Problem 2
A square-shaped building measuring 676 square feet is built; if each of the sides is √676, what will be the square feet of half of the building?
338 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 676 by 2 = we get 338.
So half of the building measures 338 square feet.
Problem 3
Calculate √676 x 5.
130
Explanation
The first step is to find the square root of 676, which is 26.
The second step is to multiply 26 with 5.
So 26 x 5 = 130.
Problem 4
What will be the square root of (400 + 276)?
The square root is 26.
Explanation
To find the square root, we need to find the sum of (400 + 276).
400 + 276 = 676, and then √676 = 26.
Therefore, the square root of (400 + 276) is ±26.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √676 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as 128 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√676 + 38)
= 2 × (26 + 38)
= 2 × 64
= 128 units.
FAQ on Square Root of 676
1.What is √676 in its simplest form?
2.Mention the factors of 676.
3.Calculate the square of 26.
4.Is 676 a prime number?
5.676 is divisible by?
6.How does learning Algebra help students in Australia make better decisions in daily life?
7.How can cultural or local activities in Australia support learning Algebra topics such as Square Root of 676?
8.How do technology and digital tools in Australia support learning Algebra and Square Root of 676?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for the Square Root of 676
- Square root: A square root is the inverse of a square. Example: 5² = 25, and the inverse of the square is the square root, which is √25 = 5.
- Rational number: A rational number is a number that can be written in the form of p/q, where q is not equal to zero and p and q are integers.
- Perfect square: A perfect square is a number that is the square of an integer. For example, 676 is a perfect square because it is 26².
- Integer: An integer is a whole number that can be positive, negative, or zero. For example, -5, 0, and 3 are integers.
- Perimeter: The perimeter is the total distance around a two-dimensional shape.
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Jaskaran Singh Saluja
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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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