126 LearnersLast updated on May 26th, 2025
Square Root of 629
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 various fields such as engineering, physics, and finance. Here, we will discuss the square root of 629.
What is the Square Root of 629?
The square root is the inverse of the square of a number. 629 is not a perfect square. The square root of 629 is expressed in both radical and exponential form. In radical form, it is expressed as √629, whereas in exponential form it is expressed as (629)^(1/2). √629 ≈ 25.079872, 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 629
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 629 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 629 is broken down into its prime factors:
Step 1: Finding the prime factors of 629 629 is a semi-prime number and can be broken down as 17 x 37.
Step 2: Now we found out the prime factors of 629. The second step is to make pairs of those prime factors. Since 629 is not a perfect square, the digits of the number can’t be grouped in pairs.
Therefore, calculating 629 using prime factorization is not feasible for finding its square root.
Square Root of 629 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 629, we need to group it as 29 and 6.
Step 2: Now we need to find n whose square is less than or equal to 6. We can say n is ‘2’ because 2 x 2 = 4 is less than 6. Now the quotient is 2, and after subtracting 4 from 6, the remainder is 2.
Step 3: Now let us bring down 29, which is 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 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 x n ≤ 229. Let us consider n as 5, now 4 x 5 x 5 = 225.
Step 6: Subtract 225 from 229; the difference is 4, and the quotient is 25.
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 400.
Step 8: Now we need to find the new divisor that is 502 because 502 x 8 = 4016.
Step 9: Subtracting 4016 from 40000, we get the result 3984.
Step 10: Now the quotient is 25.08.
Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.
So the square root of √629 is approximately 25.08.
Square Root of 629 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 629 using the approximation method.
Step 1: Now we have to find the closest perfect squares of √629. The smallest perfect square less than 629 is 625 (25^2) and the largest perfect square greater than 629 is 6400 (80^2). √629 falls somewhere between 25 and 26.
Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Applying the formula (629 - 625) / (676 - 625) = 0.08 Using the formula, we identified the decimal point of our square root. The next step is adding the value we got initially to the decimal number, which is 25 + 0.08 = 25.08, so the square root of 629 is approximately 25.08.
Common Mistakes and How to Avoid Them in the Square Root of 629
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, √50 = 7.07, there is also -7.07 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, √(12+24) = √12 + √24 is the wrong method of using roots. The right way of using roots 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 ≈ 7.071067.
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, which results in a wrong answer at the end of the sum. This may either happen in subtracting or elsewhere.
Square Root of 629 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √629?
The area of the square is approximately 629 square units.
Explanation
The area of the square = side^2.
The side length is given as √629.
Area of the square = side^2 = √629 x √629 = 629.
Therefore, the area of the square box is approximately 629 square units.
Problem 2
A square-shaped building measuring 629 square feet is built; if each of the sides is √629, what will be the square feet of half of the building?
314.5 square feet.
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 629 by 2 = we get 314.5.
So half of the building measures 314.5 square feet.
Problem 3
Calculate √629 x 5.
Approximately 125.4.
Explanation
The first step is to find the square root of 629, which is approximately 25.08, the second step is to multiply 25.08 by 5.
So 25.08 x 5 ≈ 125.4.
Problem 4
What will be the square root of (625 + 4)?
The square root is 25.08.
Explanation
To find the square root, we need to find the sum of (625 + 4).
625 + 4 = 629, and then √629 ≈ 25.08.
Therefore, the square root of (625 + 4) is approximately ±25.08.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √629 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 126.16 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√629 + 38)
= 2 × (25.08 + 38)
= 2 × 63.08
= 126.16 units.
FAQ on Square Root of 629
1.What is √629 in its simplest form?
2.Mention the factors of 629.
3.Calculate the square of 629.
4.Is 629 a prime number?
5.629 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 629?
8.How do technology and digital tools in Australia support learning Algebra and Square Root of 629?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for the Square Root of 629
- Square root: A square root is the inverse of a square. For 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, q is not equal to zero, and p and q are integers.
- Radical form: The expression of a number under a root symbol, such as √629, is referred to as the radical form.
- Perfect square: A perfect square is a number that can be expressed as the product of an integer with itself, such as 25 (5 x 5).
- Long division method: A method used to find the square root of non-perfect squares by dividing and finding the remainder in steps.
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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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