123 LearnersLast updated on May 26th, 2025
Square Root of 663
If a number is multiplied by itself, 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 663.
What is the Square Root of 663?
The square root is the inverse of the square of a number. 663 is not a perfect square. The square root of 663 is expressed in both radical and exponential forms. In the radical form, it is expressed as √663, whereas in exponential form, it is (663)^(1/2). √663 ≈ 25.751, 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 663
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 663 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 663 is broken down into its prime factors.
Step 1: Finding the prime factors of 663 Breaking it down, we get 3 x 13 x 17.
Step 2: Now we found out the prime factors of 663. The next step is to make pairs of those prime factors. Since 663 is not a perfect square, the digits of the number can’t be grouped in pairs.
Therefore, calculating 663 using prime factorization is not straightforward.
Square Root of 663 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 663, we group them as 63 and 6.
Step 2: Now, we need to find n whose square is ≤ 6. We can say n = 2 because 2^2 = 4 is less than 6. The quotient is 2, and after subtracting, the remainder is 2.
Step 3: Now, let us bring down 63, making the new dividend 263. Add the old divisor with the same number: 2 + 2 = 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 ≤ 263. Let us consider n as 5; now, 45 × 5 = 225.
Step 6: Subtract 225 from 263; the difference is 38, 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 3800.
Step 8: Find the new divisor, which is 509, because 509 × 7 = 3563.
Step 9: Subtracting 3563 from 3800 gives us a remainder of 237.
Step 10: Now, the quotient is 25.7.
Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose there are no decimal values; continue until the remainder is zero.
So the square root of √663 ≈ 25.75.
Square Root of 663 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 663 using the approximation method.
Step 1: We have to find the closest perfect squares around √663. The smallest perfect square less than 663 is 625, and the largest perfect square greater than 663 is 676. So, √663 falls somewhere between 25 and 26.
Step 2: Now, apply the formula: (Given number - smallest perfect square) ÷ (Greater perfect square - smallest perfect square) Using the formula: (663 - 625) ÷ (676 - 625) = 38 ÷ 51 ≈ 0.745 Using the formula, we identified the decimal part of our square root. The next step is adding the integer part we got initially to the decimal number, which is 25 + 0.745 ≈ 25.75.
So, the square root of 663 is approximately 25.75.
Common Mistakes and How to Avoid Them in the Square Root of 663
Students make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Now let us look at a few common mistakes 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 usually take only the positive square root, as it is the required one in most cases.
For example, √50 = 7.07, but 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 students make. To resolve this, we need to teach students that simplifying the numbers inside the square root is important before moving on to the next step.
For example: √(12 + 24) = √12 + √24 is a wrong method of using roots. 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 students 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 roots and square roots 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 at the end of the sum. This may happen in subtraction or elsewhere.
Square Root of 663 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √663?
The area of the square is approximately 663 square units.
Explanation
The area of the square = side^2.
The side length is given as √663.
Area of the square = side^2 = √663 × √663 = 663.
Therefore, the area of the square box is approximately 663 square units.
Problem 2
A square-shaped building measuring 663 square feet is built; if each of the sides is √663, what will be the square feet of half of the building?
331.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 663 by 2, we get 331.5.
So half of the building measures 331.5 square feet.
Problem 3
Calculate √663 × 5.
128.755
Explanation
The first step is to find the square root of 663, which is approximately 25.751.
The second step is to multiply 25.751 by 5.
So, 25.751 × 5 ≈ 128.755.
Problem 4
What will be the square root of (663 + 12)?
The square root is approximately 26.
Explanation
To find the square root, we need to find the sum of (663 + 12).
663 + 12 = 675, and then √675 ≈ 26.
Therefore, the square root of (663 + 12) is approximately ±26.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √663 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 127.502 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√663 + 38)
≈ 2 × (25.751 + 38)
≈ 2 × 63.751
≈ 127.502 units.
FAQ on Square Root of 663
1.What is √663 in its simplest form?
2.Mention the factors of 663.
3.Calculate the square of 663.
4.Is 663 a prime number?
5.663 is divisible by?
6.How does learning Algebra help students in Singapore make better decisions in daily life?
7.How can cultural or local activities in Singapore support learning Algebra topics such as Square Root of 663?
8.How do technology and digital tools in Singapore support learning Algebra and Square Root of 663?
9.Does learning Algebra support future career opportunities for students in Singapore?
Important Glossaries for the Square Root of 663
- 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, which 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.
- Perfect square: A perfect square is a number that is the square of an integer. Example: 25 is a perfect square because it is 5^2.
- Prime factorization: Prime factorization is expressing a number as the product of its prime factors. Example: The prime factorization of 18 is 2 × 3 × 3.
- Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal. For example, 7.86, 8.65, and 9.42 are decimals.
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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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