111 LearnersLast updated on May 26th, 2025
Square Root of 161
If a number is multiplied by itself, the result is a square. The inverse of squaring a number is finding its square root. The concept of square roots is applied in fields such as architecture, finance, and physics. Here, we will discuss the square root of 161.
What is the Square Root of 161?
A square root is the inverse operation of squaring a number. Since 161 is not a perfect square, its square root is expressed in both radical and exponential forms. In radical form, it is expressed as √161, whereas in exponential form it is expressed as (161)(1/2). The square root of 161 is approximately 12.6886, which is an irrational number because it cannot be expressed as a simple fraction p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 161
For non-perfect square numbers, methods like the long division method and approximation method are used. Let's explore these methods:
- Long division method
- Approximation method
Square Root of 161 by Long Division Method
The long division method is used for finding the square roots of non-perfect square numbers. Here's how to find the square root of 161 using this method:
Step 1: Begin by setting up the number in pairs from right to left. For 161, it will be grouped as 61 and 1.
Step 2: Find a number n whose square is less than or equal to 1. The number n is 1 because 1^2 is less than or equal to 1. The quotient is 1, and the remainder is 0 after subtracting 1.
Step 3: Bring down 61 to form the new dividend. Add the previous divisor (1) to itself to get 2, which becomes the new divisor.
Step 4: Find n such that 2n × n ≤ 61. If n is 3, then 23 × 3 = 69, which is greater than 61. Try n = 2, then 22 × 2 = 44.
Step 5: Subtract 44 from 61 to get a remainder of 17. The quotient is now 12.
Step 6: Add a decimal point and bring down 00 to the remainder to make it 1700.
Step 7: The new divisor is 24 (old divisor 22 plus n), and this process continues to find more precise values.
The approximate square root of 161 using the long division method is 12.688.
Square Root of 161 by Approximation Method
The approximation method is another way to find square roots. Let's find the square root of 161 using this method:
Step 1: Identify the perfect squares closest to 161. The smallest is 144, and the largest is 169. Thus, √161 lies between 12 and 13.
Step 2: Apply the approximation formula: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square). Calculation: (161 - 144) / (169 - 144) = 17 / 25 = 0.68 Add this to the lower perfect square root: 12 + 0.68 = 12.68
So, the square root of 161 is approximately 12.68.
Common Mistakes and How to Avoid Them in the Square Root of 161
Students often make mistakes when calculating square roots, such as ignoring the negative square root or skipping steps in methods like long division. Let's examine some common mistakes.
Mistake 1
Forgetting about the negative square root
It's crucial to remember that numbers have both positive and negative square roots. However, the positive square root is typically used in practical applications.
For example, √50 = ±7.071, but often only the positive root is considered.
Square Root of 161 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √161?
The area of the square is approximately 161 square units.
Explanation
The area of a square = side².
The side length is given as √161.
Area = (√161)²
= 161 square units.
Problem 2
A square-shaped building measuring 161 square feet is built; if each of its sides is √161, what will be the square feet of half of the building?
80.5 square feet
Explanation
To find half the area of the building, simply divide the total area by 2. 161 ÷ 2 = 80.5 square feet.
Problem 3
Calculate √161 x 5.
Approximately 63.44
Explanation
First, find the square root of 161, which is approximately 12.688.
Then multiply it by 5. 12.688 x 5 ≈ 63.44
Problem 4
What will be the square root of (138 + 23)?
The square root is 13.
Explanation
First, find the sum of (138 + 23). 138 + 23 = 161.
The square root of 161 is approximately 12.688, rounded to 13 for simplicity.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √161 units and the width ‘w’ is 39 units.
The perimeter of the rectangle is approximately 103.38 units.
Explanation
Perimeter of a rectangle = 2 × (length + width)
Perimeter = 2 × (√161 + 39)
= 2 × (12.688 + 39)
≈ 103.38 units.
FAQ on Square Root of 161
1.What is √161 in its simplest form?
2.Mention the factors of 161.
3.Calculate the square of 161.
4.Is 161 a prime number?
5.161 is divisible by?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Square Root of 161?
8.How do technology and digital tools in United States support learning Algebra and Square Root of 161?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for the Square Root of 161
- Square root: The operation that finds a number which, when multiplied by itself, gives the original number. For example, the square root of 25 is 5 because 5 x 5 = 25.
- Irrational number: A number that cannot be expressed as a simple fraction. Its decimal form is non-repeating and non-terminating, such as √161.
- Perfect square: A number that is the square of an integer. For example, 144 is a perfect square because it is 12².
- Radical: The symbol (√) used to denote the square root or nth root of a number.
- Approximation: A value or number that is close to but not exactly equal to the exact value, often used for irrational numbers like √161.
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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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