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326 LearnersLast updated on August 5, 2025
Square Root of 0.628
What is the Square Root of 0.628?
The square root is the inverse of the square of the number. 0.628 is not a perfect square. The square root of 0.628 is expressed in both radical and exponential form. In the radical form, it is expressed as √0.628, whereas (0.628)^(1/2) in the exponential form. √0.628 ≈ 0.7925, 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 0.628
For non-perfect square numbers, methods like the long-division method and approximation method are used. Let us now learn the following methods:
- Long division method
- Approximation method
Square Root of 0.628 by Long Division Method
The long division method is particularly used for non-perfect square numbers. Let us now learn how to find the square root using the long division method, step by step.
Step 1: To begin with, consider 0.628 as 628/1000. Group the numbers from right to left.
Step 2: Find n such that n² is close to 0.6. Here, n is 0.7 because 0.7² = 0.49, which is less than 0.6.
Step 3: Subtract 0.49 from 0.6, bringing down two zeros to make it 1100. The new dividend is 1100.
Step 4: Double the quotient 0.7, which gives us 1.4. Now determine the next digit of the divisor.
Step 5: Find 1.4n × n ≤ 1100. Let n be 0.8, so 1.48 × 0.8 = 1.184 (for precision, consider decimals).
Step 6: Subtract 1.184 from 1.100 (adjust with decimals) to get the remainder.
Step 7: Continue the process to achieve the desired decimal places.
The square root of 0.628 is approximately 0.7925.
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Square Root of 0.628 by Approximation Method
The approximation method is another way to find the 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 0.628 using the approximation method.
Step 1: Identify the closest perfect squares around 0.628. The closest are 0.49 (0.7²) and 1 (1²).
Step 2: Apply the linear approximation formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (0.628 - 0.49) / (1 - 0.49) ≈ 0.2706.
Step 3: Add the result to the smallest integer square root: 0.7 + 0.2706 ≈ 0.7925.
Thus, the square root of 0.628 is approximately 0.7925.
Common Mistakes and How to Avoid Them in the Square Root of 0.628
Students can make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Let us look at a few common mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to remember that a number has both positive and negative square roots. However, we generally take only the positive square root as it is more commonly used.
For example, √0.628 ≈ 0.7925, but there is also -0.7925.
Mistake 2
Not adding the square root symbol in proper places
Not using the square root symbol properly is a common mistake. Ensure that students simplify the numbers inside the square root before moving on.
For example, √(0.4 + 0.2) = √0.6 is correct, not √0.4 + √0.2.
Mistake 3
Not finding the correct value of a non-perfect square
Students should first simplify the numbers inside the square root. This avoids mistakes in identifying the approximate value.
For example, √0.7 ≈ 0.837, not 0.7.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps. Students might skip steps accidentally, leading to incorrect answers. This may happen in subtraction or elsewhere.
Square Root of 0.628 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √0.5?
The area of the square is 0.25 square units.
Explanation
The area of the square = side².
The side length is given as √0.5.
Area of the square = side² = √0.5 × √0.5 = 0.5 × 0.5 = 0.25.
Therefore, the area of the square box is 0.25 square units.
Problem 2
A square-shaped plot measures 0.628 square meters. If each side is √0.628, what will be the square meters of half of the plot?
0.314 square meters
Explanation
Divide the given area by 2, as the plot is square-shaped. Dividing 0.628 by 2, we get 0.314. So half of the plot measures 0.314 square meters.
Problem 3
Calculate √0.628 × 5.
3.9625
Explanation
First, find the square root of 0.628, which is approximately 0.7925, then multiply 0.7925 by 5. So, 0.7925 × 5 = 3.9625.
Problem 4
What will be the square root of (0.4 + 0.228)?
The square root is approximately 0.7925.
Explanation
To find the square root, first find the sum of (0.4 + 0.228). 0.4 + 0.228 = 0.628, and then √0.628 ≈ 0.7925.
Therefore, the square root of (0.4 + 0.228) is approximately ±0.7925.
Problem 5
Find the perimeter of the rectangle if its length 'l' is √0.5 units and the width 'w' is 0.3 units.
The perimeter of the rectangle is approximately 2.184 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√0.5 + 0.3) ≈ 2 × (0.707 + 0.3) = 2 × 1.007 = 2.014 units.
FAQ on Square Root of 0.628
1.What is √0.628 in its simplest form?
2.Is 0.628 a perfect square?
3.Calculate the square of 0.628.
4.Is 0.628 a rational number?
5.Is √0.628 an irrational number?
Important Glossaries for the Square Root of 0.628
- Square root: The square root of a number is a value that, when multiplied by itself, gives the original number. Example: 0.7 × 0.7 = 0.49, so √0.49 = 0.7.
- Irrational number: A number that cannot be written as a simple fraction; its decimal form is non-repeating and non-terminating.
- Rational number: A number that can be expressed as a fraction with integers in the numerator and a non-zero integer in the denominator.
- Decimal: A number that includes a whole number and a fractional part, separated by a decimal point. Example: 0.7925.
- Long division method: A method used to calculate the square root of a number by dividing the number into pairs of digits from right to left and finding successive approximations.
Vikrant Sharma
About the Author
Vikrant Sharma 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.
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