123 LearnersLast updated on May 26th, 2025
Square Root of 662
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 fields like vehicle design, finance, etc. Here, we will discuss the square root of 662.
What is the Square Root of 662?
The square root is the inverse of the square of the number. 662 is not a perfect square. The square root of 662 is expressed in both radical and exponential form. In the radical form, it is expressed as √662, whereas (662)^(1/2) in the exponential form. √662 ≈ 25.72936, 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 662
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where long-division and approximation methods are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 662 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 662 is broken down into its prime factors:
Step 1: Finding the prime factors of 662 Breaking it down, we get 2 × 331: 2^1 × 331^1
Step 2: Now we found out the prime factors of 662. Since 662 is not a perfect square, calculating its square root using prime factorization is not straightforward.
Square Root of 662 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 662, we group it as 62 and 6.
Step 2: Now we need to find n whose square is closest to 6. We can say n as ‘2’ because 2 × 2 is 4, which is less than or equal to 6. Now the quotient is 2, and after subtracting, the remainder is 2.
Step 3: Bring down 62, making the new dividend 262. Add the old divisor (2) to itself, giving us 4, which will be our new divisor.
Step 4: The next step is finding 4n × n ≤ 262. Let us consider n as 6, now 4 × 6 × 6 = 144.
Step 5: Subtract 144 from 262; the difference is 118.
Step 6: Since the dividend is less than the divisor, we need to add a decimal point, allowing us to add two zeroes to the dividend. Now the new dividend is 11800.
Step 7: Find the new divisor, which is 45, because 457 × 7 = 3199.
Step 8: Subtracting 3199 from 11800, we get 8601.
Step 9: Now the quotient is 25.7.
Step 10: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue until the remainder is zero.
So the square root of √662 is approximately 25.73.
Square Root of 662 by Approximation Method
Approximation method is another method for finding 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 662 using the approximation method.
Step 1: Now we have to find the closest perfect square of √662. The smallest perfect square less than 662 is 625, and the largest perfect square greater than 662 is 676. √662 falls somewhere between 25 and 26.
Step 2: Now we need to apply the formula: (Given number - smaller perfect square) / (Greater perfect square - smaller perfect square). Using the formula (662 - 625) ÷ (676 - 625) = 37/51 ≈ 0.72549.
Step 3: Add the initial value to the decimal number: 25 + 0.73 = 25.73, so the square root of 662 is approximately 25.73.
Common Mistakes and How to Avoid Them in the Square Root of 662
Students often make mistakes while finding the square root, such as forgetting about the negative square root, skipping steps in the long division method, etc. Let's look at a few of these mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number has 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, but 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 symbol 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 a 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; 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, resulting in a wrong answer at the end. This may happen in subtracting or elsewhere.
Square Root of 662 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √662?
The area of the square is approximately 438 square units.
Explanation
The area of the square = side^2.
The side length is given as √662.
Area of the square = side^2 = √662 × √662 = 25.73 × 25.73 ≈ 438.0729.
Therefore, the area of the square box is approximately 438 square units.
Problem 2
A square-shaped building measuring 662 square meters is built; if each of the sides is √662, what will be the square meters of half of the building?
331 square meters
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 662 by 2 = 331.
So half of the building measures 331 square meters.
Problem 3
Calculate √662 × 5.
128.65
Explanation
The first step is to find the square root of 662, which is approximately 25.73.
The second step is to multiply 25.73 by 5.
So 25.73 × 5 = 128.65.
Problem 4
What will be the square root of (662 + 14)?
The square root is approximately 26.
Explanation
To find the square root, we need to find the sum of (662 + 14).
662 + 14 = 676, and √676 = 26.
Therefore, the square root of (662 + 14) is ±26.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √662 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 127.46 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√662 + 38)
= 2 × (25.73 + 38)
= 2 × 63.73
≈ 127.46 units.
FAQ on Square Root of 662
1.What is √662 in its simplest form?
2.Mention the factors of 662.
3.Calculate the square of 662.
4.Is 662 a prime number?
5.662 is divisible by?
6.How does learning Algebra help students in Indonesia make better decisions in daily life?
7.How can cultural or local activities in Indonesia support learning Algebra topics such as Square Root of 662?
8.How do technology and digital tools in Indonesia support learning Algebra and Square Root of 662?
9.Does learning Algebra support future career opportunities for students in Indonesia?
Important Glossaries for the Square Root of 662
- 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.
- Principal square root: A number has both positive and negative square roots; however, it is always the positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as a principal square root.
- Approximation method: A method of finding the square root by identifying the closest perfect squares and estimating the value between them.
- Long division method: A systematic procedure of dividing a number to find its square root, especially useful for non-perfect squares.
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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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