109 LearnersLast updated on May 26th, 2025
Square Root of 173
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 various fields such as architecture, finance, and more. Here, we will discuss the square root of 173.
What is the Square Root of 173?
The square root is the inverse operation of squaring a number. 173 is not a perfect square. The square root of 173 is expressed in both radical and exponential form. In radical form, it is expressed as √173, whereas in exponential form it is expressed as (173)(1/2). √173 ≈ 13.152, 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 173
The prime factorization method is typically used for perfect square numbers. However, for non-perfect square numbers like 173, the long division method and approximation method are used. Let's learn about the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 173 by Prime Factorization Method
Prime factorization involves expressing a number as a product of its prime factors.
However, 173 is a prime number itself, and there are no repeated prime factors to pair.
Therefore, calculating √173 using the prime factorization method is not applicable.
Square Root of 173 by Long Division Method
The long division method is used for non-perfect square numbers. This method involves finding pairs of digits and then estimating the square root step by step.
Step 1: Start by pairing the digits from right to left. For 173, pair as 1 and 73.
Step 2: Find the largest number whose square is less than or equal to 1. This number is 1. Subtract 1 from 1, leaving a remainder of 0.
Step 3: Bring down the next pair of digits, 73, forming the new dividend.
Step 4: Double the quotient (1), giving a new divisor of 2. Find a number n such that 2n × n ≤ 73. The number is 3 since 23 × 3 = 69.
Step 5: Subtract 69 from 73, which results in a difference of 4.
Step 6: Since the remainder is less than the divisor, add a decimal point and bring down two zeros to get 400.
Step 7: Double the current quotient (13) to get 26. Find the number n such that 26n × n ≤ 400. The number is 1 since 261 × 1 = 261.
Step 8: Subtract 261 from 400, which leaves a remainder of 139.
Step 9: Continue this process to get more decimal places until the desired precision. The result is that √173 ≈ 13.152.
Square Root of 173 by Approximation Method
The approximation method provides a quick way to estimate square roots. Let's find the square root of 173 using this method.
Step 1: Identify the closest perfect squares around 173. These are 169 (13²) and 196 (14²). √173 lies between 13 and 14.
Step 2: Use the formula: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square). Applying the formula: (173 - 169) / (196 - 169) = 4 / 27 ≈ 0.148 Add this decimal to the smaller root: 13 + 0.148 = 13.148
Therefore, √173 ≈ 13.148.
Common Mistakes and How to Avoid Them in the Square Root of 173
Students often make mistakes when finding square roots, such as forgetting about negative square roots or skipping steps in the long division method. Here are some common mistakes to avoid.
Mistake 1
Forgetting about the negative square root
It's important to remember that a number has both a positive and negative square root. However, we typically focus on the positive square root for practical applications.
For example, √50 ≈ 7.07, but there's also -7.07.
Square Root of 173 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √173?
The area of the square is 173 square units.
Explanation
The area of a square = side².
The side length is given as √173.
Area = side²
= √173 × √173
= 173.
Therefore, the area of the square box is 173 square units.
Problem 2
A square-shaped garden measuring 173 square feet is built; if each of the sides is √173, what will be the square feet of half of the garden?
86.5 square feet
Explanation
To find half the area of the garden, divide the total area by 2.
Dividing 173 by 2 gives us 86.5.
So half of the garden measures 86.5 square feet.
Problem 3
Calculate √173 × 5.
65.76
Explanation
First, find the square root of 173, which is approximately 13.152.
Then multiply 13.152 by 5.
So, 13.152 × 5 ≈ 65.76.
Problem 4
What will be the square root of (169 + 4)?
The square root is 13.
Explanation
To find the square root, calculate the sum (169 + 4). 169 + 4 = 173, and then √173 ≈ 13.152.
For simplicity, we approximate to the closest whole number, which is 13.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √173 units and the width ‘w’ is 30 units.
The perimeter of the rectangle is approximately 86.304 units.
Explanation
Perimeter of a rectangle = 2 × (length + width).
Perimeter = 2 × (√173 + 30)
= 2 × (13.152 + 30)
= 2 × 43.152
= 86.304 units.
FAQ on Square Root of 173
1.What is √173 in its simplest form?
2.What are the factors of 173?
3.Calculate the square of 173.
4.Is 173 a prime number?
5.173 is divisible by?
6.How does learning Algebra help students in India make better decisions in daily life?
7.How can cultural or local activities in India support learning Algebra topics such as Square Root of 173?
8.How do technology and digital tools in India support learning Algebra and Square Root of 173?
9.Does learning Algebra support future career opportunities for students in India?
Important Glossaries for the Square Root of 173
- Square root: A square root is the inverse of squaring a number. For example, 4² = 16, and the inverse operation is √16 = 4.
- Irrational number: An irrational number cannot be expressed as a simple fraction. For example, √173 is irrational because it cannot be written as p/q, where p and q are integers.
- Prime number: A prime number has only two factors: 1 and itself. For example, 173 is a prime number.
- Decimal: A decimal is a number that includes a whole number and a fractional part. For example, 13.152 is a decimal.
- Long division method: A method used to find square roots of non-perfect squares by dividing and estimating step by step.
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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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