119 LearnersLast updated on May 26th, 2025
Square Root of 160000
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 160000.
What is the Square Root of 160000?
The square root is the inverse of the square of the number. 160000 is a perfect square. The square root of 160000 is expressed in both radical and exponential form. In the radical form, it is expressed as √160000, whereas (160000)^(1/2) in the exponential form. √160000 = 400, 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 160000
The prime factorization method is used for perfect square numbers. For perfect squares like 160000, both the prime factorization method and the long division method can be used. Let us now learn the following methods:
- Prime factorization method
- Long division method
Square Root of 160000 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 160000 is broken down into its prime factors.
Step 1: Finding the prime factors of 160000. Breaking it down, we get 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5: 2^6 × 5^4
Step 2: Now we found out the prime factors of 160000. The second step is to make pairs of those prime factors. Since 160000 is a perfect square, the digits of the number can be grouped in pairs. Therefore, calculating √160000 using prime factorization is possible.
Step 3: The square root is obtained by taking one number from each pair, so √160000 = 2^3 × 5^2 = 8 × 25 = 200.
Square Root of 160000 by Long Division Method
The long division method is particularly useful for both perfect and 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 160000, we group it as 16 and 0000.
Step 2: Now we need to find n whose square is less than or equal to 16. We can say n is 4 because 4 × 4 = 16. Now the quotient is 4, and the remainder is 0.
Step 3: Bring down the next pair of zeros, making the new dividend 0000, and bring down another pair making it 000000.
Step 4: The divisor is now 80 (2 × 40) and bringing down the 0s does not change anything as they are zeros. Step 5: Therefore, √160000 = 400.
Approximating the Square Root of 160000
For a perfect square like 160000, approximation is not needed, but if the number were not a perfect square, approximation methods could be used.
Common Mistakes and How to Avoid Them in the Square Root of 160000
Students do make mistakes while finding the square root, like forgetting about the negative square root or skipping the long division method. Now let us look at a few of those mistakes that students tend to make in detail.
Common Mistakes and How to Avoid Them in the Square Root of 160000
Students do make mistakes while finding the square root, like forgetting about the negative square root or skipping long division methods. Here are a few mistakes and how to avoid them.
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 typically consider only the positive square root, as it is the required one in most real-world applications.
For example: √2500 = 50, but there is also -50, which should not be forgotten.
Mistake 2
Not adding the square root symbol in proper places
Misplacing the square root symbol is a common mistake. To avoid this, it's essential to teach students the proper order of operations.
For example: √(16 + 64) ≠ √16 + √64; the correct method is √(16 + 64) = √80.
Mistake 3
Not finding the correct value of a non-perfect square
For non-perfect squares, approximate values must be calculated carefully.
For example, √200 ≈ 14.142, not 14.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube roots and square roots consistently.
For example: √64 and ∛64 are different; √64 = 8 and ∛64 = 4.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps. Skipping a step can lead to incorrect results. Careful practice and attention to each step can prevent these errors.
Square Root of 160000 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √160000?
The area of the square is 160000 square units.
Explanation
The area of a square = side^2.
The side length is given as √160000.
Area of the square = side^2 = √160000 × √160000 = 400 × 400 = 160000
Therefore, the area of the square box is 160000 square units.
Problem 2
A square-shaped building measuring 160000 square feet is built; if each of the sides is √160000, what will be the square feet of half of the building?
80000 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 160000 by 2 = 80000
So half of the building measures 80000 square feet.
Problem 3
Calculate √160000 × 5.
2000
Explanation
The first step is to find the square root of 160000, which is 400. The second step is to multiply 400 by 5. So 400 × 5 = 2000.
Problem 4
What will be the square root of (160000 + 40000)?
The square root is 447.21
Explanation
To find the square root, we need to find the sum of (160000 + 40000) 160000 + 40000 = 200000, and then √200000 ≈ 447.21. Therefore, the square root of (160000 + 40000) is approximately ±447.21.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √160000 units and the width ‘w’ is 200 units.
We find the perimeter of the rectangle as 1200 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√160000 + 200) = 2 × (400 + 200) = 2 × 600 = 1200 units.
FAQ on Square Root of 160000
1.What is √160000 in its simplest form?
2.Mention the factors of 160000.
3.Calculate the square of 160000.
4.Is 160000 a prime number?
5.160000 is divisible by?
6.How does learning Algebra help students in Thailand make better decisions in daily life?
7.How can cultural or local activities in Thailand support learning Algebra topics such as Square Root of 160000?
8.How do technology and digital tools in Thailand support learning Algebra and Square Root of 160000?
9.Does learning Algebra support future career opportunities for students in Thailand?
Important Glossaries for the Square Root of 160000
- Square root: A square root is the inverse of squaring a number. Example: 20^2 = 400, and the inverse is √400 = 20.
- 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. Example: 160000 is a perfect square because it is 400 squared.
- Divisor: A divisor is a number that divides another number completely without leaving a remainder.
- Prime factorization: Prime factorization is the process of expressing a number as a product of its prime factors.
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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
: He loves to play the quiz with kids through algebra to make kids love it.
